[Stefan-A]

We're not simply talking about a wild population, we are talking about a wild population that's already declining due to a lack of resources (habitat, for example) and then suddenly subjected to increased competition for those resources. The carrying capacity would be exceeded even further and the population would collapse as a result.

First, the amount of resources would plummet and the mortality rate would skyrocket as a result. That alone can make the population collapse. If that doesn't happen, you'll still have a population with a need to migrate and because of the previous sudden increase in the use of the resources in the area, the area would now be able to hold even fewer individuals than before, exacerbating their situation. And fewer individuals could very well lead to the population reaching that critical level.

But if the habitat is restored, the population will recover on its own, at a more reasonable rate. Provided that there still are enough individuals left.