Does the borrower’s obligations to the institution continue after the institution is closed?

Yes. When acting as Liquidator of a closed institution, the DIC is acting on behalf of all creditors of that institution and its obligation is to collect on all loans promptly and efficiently along with other assets of the institution.  

Will the Corporation offset a deposit balance held by a customer against the balance due on the loan?

The Corporation will offset the balance on a deposit account, including any uninsured portion, against a loan if the loan and deposit are held by the same person or persons.