Great questions Beruby!
Foreclosed homes that are rented had tenants in them prior to the foreclosure and the bank is upholding the existing lease. Generally, banks do not re-lease property that is not commercial in function. (Commerical being apartment complexes, Commercial centers, multi-plex/multi-use)
In todays market (04/05/2013) there are over 5100 homes available for rent. That is MORE than the number of homes available to buy! So there should be no problem finding a great home to rent out. I would seek the advice of a great agent to help you find a home, I'm positive there is a home just as wonderful for rent as the foreclosure you may have set your eyes on.
For those people asking this question because there home is being foreclosed on and they would like to continue living there, the bank will not allow this, but generally works with you regarding relocation. Once a home is foreclosed on an agent will work with you to set deadlines for moving. Agents are people too and understand the difficult situation. They will work with you to resolve the situation amicably. If they leave you a notice or send one in the mail, simply call them back and they will explain all the terms and conditions and in many cases help you find a beautiful property.
Have a wonderful day
Prominent Realty Group