Examples of healthy lifelong asymptomatic carrier of a severe infectious disease?
I am curious, is there any known disease/infection that is very severe normally, but ends up having little to no effect on the lives of asymptomatic carriers?


HIV is an obvious example, where so-called "long-term nonprogressors" successfully suppress HIV replication sufficiently that they do not develop AIDS but are unable to clear the infection entirely [1].  


  patient suffers greatly and die easily without medical treatment


Since the comments below seem to suggest that HIV does not cause death without medical treatment, I'll point out that this is incorrect.  Over 30 million people have died from HIV infection.  


  I am asking this as I am thinking whether this means certain disease symptoms are evolutionarily wired to protect the "greater good"


It does not.  Selection happens on individuals and not whole species, so the greater good is irrelevant.  Asymptomatic infection is a point on the spectrum of possible responses to infection between sterilizing immunity and death. Individuals who are chronically infected mount enough of an immune response to control the infection but not enough to completely clear it.  In the case of HIV, they are typically people who have exceptionally strong immune responses to a normally lethal virus.  

Edit

The comments below suggest a deep misunderstanding of evolution. Since I think these are really the core of your question, I'll address them here.  


  If traits really evolve only according to how much an individual reproduce sucessfully, it would be a different world today.  


Which individuals reproduce is the sole determinant of which genes are passed down to the next generation.  This is because the genetics of each individual are determined at conception, and cannot be changed.  Hence, reproduction alone determines the traits of the next generation.

To quote wikipedia[2]:


  Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes that are passed on from parent to offspring during reproduction. Different characteristics tend to exist within any given population as a result of mutation, genetic recombination and other sources of genetic variation. Evolution occurs when evolutionary processes such as natural selection (including sexual selection) and genetic drift act on this variation, resulting in certain characteristics becoming more common or rare within a population


Evolution is the process by which some traits are passed down to the next generation while others are not though the mechanisms of selection (e.g. individuals with harmful traits dying) and genetic drift (e.g. random chance). 


  Thank about a hypothetical super fast reproducing bacteria, using up all resources, which means extinction at the end, such traits would not be passed on. In fact some sort of "moderation" mechanism is needed to take care of the "greater good".


This is exactly what happens if you put a lot of fast reproducing bacteria in a closed environment with limited resources.  They will all eventually die. 

You seem to be thinking of evolution as something that intelligently looks out for the wellbeing of species.  This is not the case.  Evolution is a random process by which different amounts of reproduction and survival between individuals alters the composition of the succeeding generations. As a random, emergent process it has no goals, no intelligence, and no sense of "good".  Rather, it simply happens as a result of individuals reproducing.  This frequently does lead to extinction, as evidenced by the fact that the vast majority of species no longer exist.  

(1) https://academic.oup.com/cid/article/51/2/239/303856
(1) https://en.wikipedia.org/wiki/Evolution