Payments against a mortgage need to be made by someone, be it parents or child, if either party wants to keep the Deed to the house.
Future mortgage payments could be withheld, but the mortgage holder will certainly foreclose on the property and take Deed to the home through the courts.
The mortgage holder has first rights to any property not owned outright, regardless of the name on the Deed.
In many cases, such a change to the Deed without the consent of the mortgage holder can actually force immediate and full payment of the mortgage balance due; the mortgage documents should be reviewed carefully.
The house also could be sold, and the cash generated from such a sale can be used to complete the mortgage payments due.