The tenant was paying rent to the previous owner but hasn't been paying rent for a while since the property was foreclosed and sold to the bank.

It may create a problem for you later if your bank discovers the account is owned by an LLC that no longer exists.

@Penny WilkinsonIf there are no comps, then I would try to ask community banks what they would be able to lend on it.

I would, If in this position, take the equity in the form of a HELOC and purchase a cash flowing asset that would not only pay for itself but pay for the cost of the money while putting cash into my bank account each month. 

@Charles Kao I believe he means attorney & Title Services that are familiar with non traditional or creative Transfers or Sales of property that don't include Banks.

This is already going on in banking.

A traditional bank will not give a line of credit even if there is significant equity because it boils down to being able to pay back the money. 

Bossier partner managed property and repairs while we managed business structure and banking account setup.

If you have bank loan (not an agency loan) or no mortgage at all, an LLC is certainly an option.

Many banks limit personal loan amounts.