banks do not generally rent their residential foreclosure property. It is more important for them to get the property off of their books and reloan the money.

No, banks are not equipped to be landlords.

I have never heard of a bank willing to rent a property to new tennants after a foreclosure. The banks are not in the Real Estate business, nor do they wish to be. Once foreclosed on they want to get the property off of the books as quickly as possible and for the most amount of money. They rely heavily on local Realtors to help them price and sell properties. Besides the majority of investors looking to buy these properties want them delivered empty of tennants.

They will rarely rent single family homes. Like almost never. They occasionally will allow tenants to remain in duplexes, triplexes, fourplexes and they will often allow tenants to stay in multifamily complexes and in commercial properties.

This stems from the bank defaulted assets managers beliefs and opinions that cold vacant houses with the water shut off, windows boarded up, grass turning to weeds, and pools turning green are more attractive to buyers than properties with families living in them, will sell quicker and for higher prices.
The bankers are wrong to believe this (in my humble opinion) ,