During a recession, like that of 2007, what happens to apartment complexes and their rental rates?

Obviously, the housing market collapses because people lose their jobs and can't buy houses. But people still need a place to stay.

I once heard that rental rates actually increase during a recession because the demand for rental housing increases (because no one is buying houses). Is this true?

No matter how bad the recession/depression, people still need a place to live.