Very rarely. Banks don't want to be landlords and more than 95% of properties taken to foreclosure right now go back to the bank. Most auction investors also prefer not to rent back.

thank you - helps greatly with a decision

You can always go to the sale and see if its bought by a third party, you can let them know you want to rent, propose a rental amount, and see if you can't negotiate a deal on the spot.  I have represented some investors buying a auction that do want tenants, and if you have the money for a deposit and rent, they may take up your offer.  It's a longshot, but you never know unless you try.  You have to make it easy and worthwhile for them.