Deallen's explanation is only partially correct. It all depends on the county, but once a house has been sold at auction whether to 3rd party or back to the bank, the prior owner has absolutely no rights to the property.
However, all the winning bidder has is a certificate of sale and an "equitable interest" in the property. Once its bought, court usually takes 90 days to approve the sale, at which the sheriff will force eviction with the prior owner WITHIN 30 DAYS OF THAT APPROVAL. That is where Deallen is incorrect, their is NO eviction process at that point. The "cash for key's" concept is really to give the owner money not to trash the home and assist in their moving out.