Is there a mental condition that makes people unconditionally gullible? The last several years in my country there has been a string of fraud that involves people, claiming to be police, asking citizens to contribute large sums of money to aid "police investigation".

The cases persist even though news about it is all over the place, leading me to presume that the whole operation might be targeting people that suffer from a specific mental condition.

When I was a child, there was this kid that you could trick literally any number times in a row, the same thing, in a sequence, just seconds apart, and it would fall for it each and every time. This memory leads me to presume that there is indeed such a condition, and that the aforementioned fraud operation targets people with that condition, so I was wondering if this kind of behavior is studied and documented.

EDIT: The answers so far focus on trust, which is understandable, since I did say "gullible", and it is an omission of my own that I didn't mention it in the initial post, but in many of those cases there is also an element of intimidation immediately prior to the request to "help catch the criminals", which probably plays a significant psychological role too, slightly expanding the context beyond just "unconditional unfounded trust".
Some neurodegenerative diseases cause extreme gullibility, in particular Alzheimer 


  Using magnetic resonance imaging (MRI), the scientists were able to determine which parts of the brain govern a person’s ability to identify sarcasm and lies.  The images revealed the associations between the deteriorations of particular parts of the brain and the inability to detect insincere speech.
  
  “These patients cannot detect lies,” said UCSF neuropsychologist Dr. Katherine Rankin, a member of the UCSF Memory and Aging Center and the senior author of the study. “This fact can help them be diagnosed earlier.”
  
  The frontal lobes are strongly associated with complex, higher-order human thinking; thus being unable to detect a lie is only one of several ways the disease may manifest itself. Early symptoms may include any number of differences in behavior, including acting out in socially inappropriate ways or experiencing fundamental shifts in beliefs — changing political views or religions, for example. 


As such brain-damage related phenomena, sometimes accidental or neurodevelopmental versions are found, but they are usually rarer.

Regarding the latter, Greenspan et al. (2001) have proposed that gullibiltiy be considered a defining characteristic of mental retardation, but their proposal is not mainstream:


  Recent efforts to redefine mental retardation (MR) have been based on the belief
  that invented scientific criteria, e.g., IQ and adaptive behavior, are insufficient to
  diagnose a disorder which over the centuries was diagnosed on the basis of intuitive
  prototypes (Greenspan, 1997). In this chapter, we argue that a central aspect of the
  MR prototype which has been largely overlooked in recent conceptualizations is
  a tendency toward unusual credulity and gullibility. In our view, it is credulity and
  gullibility, as much or more than deficiencies in daily living skills, which cause
  people with MR (and, for that matter, other forms of cognitive impairment) to be
  viewed as "disabled" and, perhaps, in need of protections such as conservatorship
  arrangements. 


Their evidence (in that paper) is mostly in form of case report series rather than more systematic. A more systematic study was conducted by Sofronoff et al. (2011) on children with Asperger syndrome (AS). This choice of subjects had the advantage that IQ effects could be separated from social intelligence. Sofronoff et al. had devised a "Social Vulnerability Questionnaire" (fairly PC name) some 4 years prior, and it turned out they could even distinguish between gullibility and credulity using their instrument, a distinction inspired from Greenspan's ideas:


  Constructs related to deficits in social intelligence are credulity and
  gullibility. Greenspan, Loughlin and Black (2001) defined credulity as ‘a
  tendency to believe something, usually a highly questionable statement or
  claim, despite scanty evidence’ (p. 102) and gullibility as ‘a vulnerability
  to being tricked or manipulated’ (p. 102). The authors stated that the two
  constructs are very closely related in that the presence of credulity invariably
  leads to a gullible outcome and that, while a tendency to be trusting
  may generally be a good and stable attribute, survival in the social world
  requires an ability to discriminate those occasional situations where
  compliance or agreement may result in an adverse outcome. The authors
  state that low social intelligence and specifically high credulity and gullibility
  may lie at the heart of poor social outcomes for children and adults
  with AS (Greenspan et al., 2001).





  Table 1 shows the items
  and their factor loadings after rotation. The two factors relate to getting
  tricked into things or bullied (factor one) and believing others’ statements to their own detriment (factor two). A Pearson’s correlation revealed the two
  factors were moderately correlated with one another, r = .519, suggesting
  that while related they are different enough to be two distinct factors.


However despite this statistical feat, the number of Asperger's children who were outright identified as gullible as fairly low, around 11% of the sample; credulity was more widespread at 23%.



Given that the SVS questionnaire invited examples from the respondents (parents)  in order to substantiate their Likert scale choices, the authors could illustrate with some snippets:


  Other areas that were mentioned by more than
  10% of parents included credulity or deception:‘believes everything other kids say,
  even if it’s wrong’ and ‘has watched TV and insisted that we buy something because the
  salesmen said “you must buy this”’; [...]
  and gullibility ‘today J threw a girl’s hat on the school roof because another child told him
  to’ and ‘told to jump in the school fish pond’.


A 2018 paper by Seward et al. was rather skeptical of Sofronoff et al.'s claim of two clear factors in children; they could not replicate the finding using a different questionnaire:


  Specifically, the first factor (gullibility) contained
  victimisation items and the second factor contained
  both credulity and gullibility items. Consequently, these
  findings raise doubt as to whether the two-factor conceptualisation
  of social vulnerability described by Greenspan
  et al. (2001) is applicable to children.
  
  The two-factor
  conceptualisation of social vulnerability (i.e., credulity and
  gullibility) proposed by Greenspan et al. (2001) did not
  emerge in the current study, even when a two-factor solution
  was forced, despite having items clearly representing
  both credulity and gullibility and a large sample with considerable
  variability. Rather, our results indicate that credulity
  and gullibility are part of the same factor, suggesting that
  the theoretical conceptualisation of social vulnerability
  described by Greenspan et al. (2001) is not applicable to
  children. It is possible that, for children, social vulnerability
  is a unitary construct, and that as individuals develop,
  the construct becomes more complex and delineates into
  two factors (credulity and gullibility) as seen in older adults
  (Pinsker et al., 2011). Further research conducted across the
  lifespan will be required to determine if this is in fact the
  case.


However Seward et al. did find something else of interest (again proposed by Greenspan) namely that gullibility/credulity wasn't the same thing as general weakness in social skill altogether:


  Furthermore, the weak negative relationship between parent
  reports of social vulnerability and prosocial behaviour
  indicates that being socially vulnerable is not simply having
  a lack of social skills, providing support for discriminant
  validity. This is consistent with Greenspan et al. (2001)
  who suggested that poor social skills are likely to contribute
  to (but are not the same thing as) being deceived
  or cheated




Regarding William's syndrome; the actual systematic research on this looks somewhat limited to me. Wikipedia does indeed claim that they are unusually trusting... but what the actual papers citedy say is...

Dykens &amp;  Rosner:


  Interest in other were seen as well in the Help Others domain, with both the Williams and Prader-Willi groups showing "strong desires to help others" and being "very happy when others do well". The Williams syndrome group, however was singularly high in the item "feels terrible when others are hurt". 


Udwin et al.


  overanxious to please and constantly seeking reassurance of satisfactory progress (34%)


Einfeldad et al. don't actually have any findings of their own in this respect, but cite Gosh an Pankau for 


  higher levels of indiscriminate friendliness


One can presumably manipulate people with Williams by playing this card... I guess this qualifies as gullible to some degree, although perhaps not as credulity. All the papers cited in Wikipedia on this are pretty old (all predate Greenspan's 2001) so maybe it's a matter of terminology. Greenspan et al. offer some commentary:


  Reis (1998), in a study of young adult women with Williams
  syndrome--a chromosomal disorder associated with mild or borderline MR---
  found that virtually 100% of them had been sexually abused by male peers or
  workers. Dykens (1998), confirming this finding, has attributed it to the extreme need to please which is an aspect of the Williams syndrome behavioral phenotype.
  While such affective and motivational factors undoubtedly are very important (see
  the multidimensional model depicted in Fig. 1), it should not be assumed that
  social-cognitive factors, such as credulity, are irrelevant. There is considerable
  research (Dykens &amp; Hodapp, 1998; Rourke, 1995) suggesting that social deficits
  in people with various syndromes are typically more significant than their academic
  deficits. Furthermore, the tendency to think of social competence primarily in terms
  of agreeableness may blind observers to the very real social intelligence deficits
  of individuals (such as most people with Williams syndrome) who are extremely
  affable and verbally facile.
  
  




And about the news stories... scamming the average person by phone is easy enough without access to health records and the like. The Bulgarian cases reminded me of the Taiwanese located in Spain or even Kenya scamming mainland Chinese with a scheme in which a caller pretend to be police asking for help. 

For contrast, Greenspan in his 2009 book has a vignette of someone with Williams syndrome... and it's much more extreme... most people can't be convinced to leave their home and sleep under a bridge:


  Larry’s need for support [from a neighborhood association] stemmed from his extreme gullibility, and the
  threat that this posed on numerous occasions to his wellbeing. Specifically,
  Larry—who lived alone—was very lonely, and he tended to befriend homeless
  people living on the street. He would give them keys so that they could use
  his bathroom or sleep in his apartment, would agree to give them money
  (when he barely had enough to make it through the month), and was even
  persuaded, until someone intervened, to run off to live under the boardwalk at
  Coney Island with one of his homeless friends. Aside from the costs to Larry
  (such as having his meager possessions repeatedly ripped off ), the presence
  of these strangers in the building—many of them with criminal backgrounds
  or severe mental illness—was very upsetting to Larry’s neighbors, who feared
  both physical damage to the building (e.g., a shower left running in Larry’s
  apartment caused major water damage) and for their own safety. Thus, the
  decision by Larry’s neighbors to create a “circle of friends” was motivated not
  only out of affection for him but also because they saw it as an alternative to
  his eviction (which had been considered at one time) and as a way to protect
  themselves and Larry from his own gullibility, a gullibility that reflected his
  cognitive limitations as well as his strong social neediness.


On the other hand, older people are apparently more susceptible to scams:


  “When emotionally aroused, either excited or frustrated, older adults may be more susceptible to being victimized by scammers than are younger individuals,” says Ian H. Gotlib, professor of psychology and author of a new report from the Center on Longevity at Stanford University.


This gives a much simpler way for scammers to profile their targets.


  Studies show that the elderly – individuals aged 60 and over – are targeted more frequently
  by financial fraud and scams than other age groups. A recent MetLife Study of Elder and
  Financial Abuse found that in 2010, $2.9 billion (yes, that’s billion with a B) was stolen from the
  elderly through financial fraud, scams, and exploitation. Additionally, research conducted by the
  Federal Trade Commission found that 80% of telemarketing scam victims are over the age of 60.