A caveat on this submission: The following essay is strictly from the perspective of a biologist's point of view on the issue. It is not meant to be a treatise endorsing eugenics or euthanasia.
HIV infection and the accompanying Acquired Immune Deficiency Syndrome (AIDS) are as far from a Darwinian means of population stabilization as any disease imaginable, unless the stabilization point is extinction. The Black Plague and The Flu Pandemic of 1918 served as population stabilizing diseases. HIV is an entirely different matter.
Some of the individuals infected with the disease are capable of continuing to indiscriminately spread HIV infections for a few years, and if treated, for an even longer time.
Those individual members of the species infected with the virus can pass the disease on to their offspring, dooming them to an early, painful death. For it to be a means for stabilizing the population, HIV would need to rapidly render its victims incapable of serving as a disease vector, then kill them; and, it would have to kill them before they had the opportunity to have another child.
An HIV-infected person will initially show no signs of the disease, unlike virtually every other lethal pandemic disease ever encountered in human history. Those infected are a vector for spreading the infection unless they take measures to never expose another person to the disease. They are invisible carriers of the disease, and those not-so infected have no readily-available signals to avoid the infected individual. The disease hides itself amongst its host.
Treating HIV infected patients promotes the spread of the disease, especially in those populations that refuse to adopt celibacy as the only means of effective prevention. By prolonging the life of an infected individual, that individual becomes a disease vector for a prolonged period, thereby giving the virus the potential for further spread.
These points are all easily seen by looking at the wildfire spread of HIV infections throughout Africa, which have been primarily brought on by a combination of a lack of education about the cause of the disease and those individuals who continue to ignore the cause. If the infected individual died before having a chance to infect multiple individuals, then yes, perhaps HIV would be a population stabilizing agent.
Without removing the carriers from the population, the end stabilization point of HIV will be an extremely stable population an extinct species' numbers are permanently fixed at zero.