In SARs and ebola, etc. When isolating people, I can only think of the viruses not spreading after the infected has died. Unless one isolated their whole life, just in case, without a vaccine I guess nature will take it's course.
Not true. This depends strongly on the specific virus.
Many are eliminated by the immune system entirely. That is, after all, the job of the immune system. When this happens, the person is 'cured' and no longer infectious. Also, usually, this results in someone who is immune from further infection: if they are exposed again, the immune system already knows how to combat that virus.
So, it is not always the case of 'once infected, always infected'. In fact, the whole notion of 'quarantine' is related to a 40 day waiting period to ensure the person is not infected or, if infected, has cleared the infection from their system.
For some viruses, even a corpse is infectious, so dying alone may not be enough to stop spread of a virus. I wouldn't recommending touching a corpse of someone who died of Ebola, for example.
Many viruses (for example Herpes) can go into remission. When that happens, the person doesn't have symptoms and is not infectious for new people, even though the virus is still in their system. The problem here is that it is possible, later, for the virus to come out of remission and the person can become infectious again. This can cycle for some viruses.
So, the way things usually play out in the absence of a vaccine: the virus spreads in the population. Either those who have it are isolated until it is cleared from their system, at which point they are free to rejoin society, OR the virus infects almost everyone, which causes a lot of death, but those who remain tend to have natural immunity (meaning their immune system knows how to fight it).
What vaccines do, in part, is build up a population of people who are immune to new infection, which leaves the virus fewer opportunities to spread. This is why there can be outbreaks when too many people don't get the vaccine: the number of susceptible people is large enough for the virus to spread more freely again.