What is the diagnosis when someone suffers only from negative symptoms of schizophrenia? If someone has almost all of the negative symptoms of schizophrenia, and no positive symptoms of schizophrenia whatsoever, is that enough to be diagnosed with a mental disorder?

I understand that a diagnosis of schizophrenia is not possible with only negative symptoms.
Short answer
Many people in the general populace suffer one or more negative symptoms that are associated with schizophrenia, but are not diagnosed with a mental illness whatsoever.

Background
Indeed, for a diagnosis of schizophrenia, negative symptoms alone are not enough. According to the Diagnostic and Statistical Manual of Mental Disorders, (DSM-5), to meet the criteria for diagnosis of schizophrenia, the patient must have experienced at least 2 of the following symptoms:


Delusions
Hallucinations
Disorganized speech
Disorganized or catatonic behavior
Negative symptoms


Werbeloff et al. (2015) note that, similar to psychotic experiences, negative symptoms are common in the general population, namely between 20–22%. The vast majority of these people do not manifest a clinically diagnosed psychiatric disorder. Negative symptoms do appear to be associated with the development of schizophrenia later in life, and to other non-psychotic disorders. However, neither negative symptoms nor psychotic experiences alone predicted later schizophrenia in their study. It was only the combined presence of both strong positive psychotic experiences and negative symptoms together that showed a statistically significant risk for later schizophrenia.

Reference
- Werbeloff et al., PLoS One (2015); 10(3): e0119852