If you stay and live in the house without paying the mortgage, you are not breaking the agreement with the lender. The lender is not a friend to whom you owe something above and beyond what was in the legal agreement each party agreed to. What you agreed when you bought the house was to EITHER keep paying the mortgage, OR stop paying and submit to the foreclosure process.
That’s it. Don’t be nice to a bank. It would never return the favor.