Unlike home prices, rents are not subjected to speculation. Usually, incomes need to go up for rents to rise.
With that said, consider the following scenario:
There is massive foreclosures & the result is a large number of SFHs & condos (some of which are formerly appartment units) being held by the lenders. These SFHs & condos are vacant. This result in a reduction in the supply of the rental units & push rents up. How realistic is this scenario ?