Could not possibly happen this way.

First,  title is reviewed initially at the time of purchase and then again on each refi. Problems with title would have surfaced long before foreclosure, and would need to have been rectified before the lender would grant a mortgage.

Another title search is ordered by the lender prior to initiating the foreclosure action to determine priorities of encumbrancers and who must be included in the suit at junior encumbrancers (defendants). Determination is made by lender as to whether to sue on the note for money damages, sue to foreclose the mortgage or both as alternate claims.

Lender insists on title insurance at the time of purchase and each refi. Title insurers again order title search to determine the state of title they are required to insure.

There are not many defenses to a foreclosure action (fraud, release, payment, etc.). if a borrower is unable to pay his mortgage, it is not likely that a claim for title defects is going to help. By that time the title has probably been searched ad nauseum  , and a defect in title would have long since surfaced.

Title insurance is a cash cow. Rarely do title insurance companies have to pay off on claims, and when they do they implead the abstractor and seek reimbursement from his e&o insurer. As usual the abstractor is on the hook...not the lender ...nor the title insurer.

Furthermore, it would be the lender not the client that would be filing the claim if the lender took title through the foreclosure. The bank would file through a lender's policy. The homeowner would file through a homeowner's policy in the event of sale. Home owner would not file in event of foreclosure. It would never be an issue in a foreclosure action.

Even if the homeowner put in a claim pursuant to the scenario you describe...it would be paid out to release the encumbrance in question. It would not go into the borrower's pocket. The title insurance company would never pay it out unless it were assured of verifying the issuance of a release in return.