Banks routinely assign mortgages to each other.  That is one reason that FHA conforming mortgage and forms are prevalent.  The banks take in application fees, points, etc., and then sell blocks of mortgages to others, at a discount. 

Legal malpractice cases, even when arising from mortgages may not be similarly traded in Florida.  Here is a case in which an attorney discontinued an earlier foreclosure in order to start a new one.  This action violated the statute of limitations, and the bank ultimately lost.  However, as they had assigned the mortgage to yet another bank, the successor bank not only lost on the foreclosure, but were unable to sue the attorney.