Could someone with Foreclosure sale experience answer the question below?  Or, at least discuss the possible outcome?

Scenario:

A homeowner has a Federal Tax lien against the property.  The homeowner is delinquent on their mortgage and it goes to Foreclosure.  At the Foreclosure sale, the property then goes back to the lender because there were no bidders for the home.

1)   Is the Lender required to pay off the Federal Tax lien at Foreclosure or resale of the home?

2)  If the Lender pays off the Federal Tax lien, what recourse does the Lender have against the borrower?

3)  If the Lender pays off the Federal Tax lien,  has the delinquent borrower just handed off their tax burden to the Lender and walked away with no liability?

Thanks!