First you need to understand the mortgage industry. The banks are the servicers not the lenders. They lend the money for the initial loan then immediately sell it to a large investor like Fannie or Freddie. You make your payment to them but they no longer own your mortgage.
The banks don’t have the money to continue holding a mortgage because they need the money back to loan it out again on new loans next month. Occasionally they will sell to another investor who may service their own loans in which case you might get a letter telling you to start sending your payment to so and so because your loan has been sold.
Most of the time if you are making your payment to Chase, Wells Fargo, Bank of America, Fifth Third etc. They are just servicing your loan. They sold it to Fannie or Freddie 30 days after you closed.
Unless the servicer also owns the loan if they take the house back due to non payment they have to assign it over to the entity that holds the note. They don’t get to keep it.