Yes, title transfers at the completion of a trustee sale. A lot of confusion comes with your question. The foreclosure process is a process that is governed by state and federal laws, followed by the policies of the lender involved.What could be true and correct in one area, may not be so in another. In addition, the foreclosure process is different based on the type of loan that is in place; for instance a note and deed of trust vs. an agreement for sale, or a mortgage.
I hope that helps.
Bye for now,