There would be 2 separate deeds. If you continue paying on the 1st, but not on the 2nd, it would be up to the 2nd note holder to foreclose, take possession, and they would have to keep up the payments on the 1st, to protect their position, which may not be worth doing.
If they didn’t foreclose, the lien would just remain on the property until something was negotiated “someday”
If the borrower stopped making payments on the 1st and 2nd, the foreclosure would be initiated by the 1st, and the 2nd may end up with nothing.
This does not address 1099 issues regarding debt relief, recourse or non-recourse debt, or the possibility of a deficiency judgment.