Foreclosing: How to handle current tenants before the auction?

[Paul Winka]

As a lender, I have a delinquent borrower that won’t pay and I’ve begun the foreclosure process. I am prepared to make this my own rental property if the auction doesn’t work out like I want. 

The house is occupied, and the tenants are paying rent to the borrower as far as I know for now. Would it be wise to approach the tenants before the auction to give them a heads up that the house is being foreclosed, maybe discuss a cash for keys scenario or continued paying of rent to me? I am trying to use the time wisely to make life easier down the line. 

I am trying to see this from tenants’ perspective, their right to quiet enjoyment, etc. A stranger knocking on the door saying the house is being foreclosed, saying he's going to be the new owner, and offering me cash to get out in a month or to give me their rent money. Sounds like a scam. I can see a situation which the tenants will say "we already paid the rent for this month to Mr. Borrower, you'll have to talk to him", even lying about it...then getting uglier from there. 

What are the best practices for what to do before a foreclosure takes place regarding an occupied house?