In Connecticut the name of the game is limitation of liability. It is rare that you will see a foreclosing lender passing title in a deed other than a quit claim deed or the limited warranty deed.

By the quit calim deed the lender conveys such title as he may have subject to whatever encumbrances are recorded on the property, and have not been foreclosed.

Through the limited warranty deed (aka a special warranty deed in some areas) the lender conveys title warranted only to those actions and conduct incurred during his period of ownership, but not prior thereto.

You are quite correct in beginning your search back at the last warranty deed (in some cases you may want to go back further). You should price your search accordingly.