The virus spreads ftom person to person. The more people that have it, the more it spreads (all other things being equal). It doesn't have a quota. If fewer people have it, then fewer people will get it.
See New Zealand. Everyone in New Zealand will eventually get it. But it will take years at their current rates. Maybe a decade. Depends on the efficacy of the vaccine. They aren't leting anyone get it. But in those years to a decade they will have outbreaks and will have to shut down again and again and again. That's not good.
Yep. The virus does not cease existing because you lock people away.