Do you have locks like this?
They’re usually called Night Latches and are pretty common in older buildings. They’re great since its only 5 screws to change the lock cylinder/key without the need for a locksmith. This one is spring loaded, so it will lock behind you (they also sell regular dead bolt versions).
However being used in older houses and given that their latch is spring loaded (slam, slam, lock?) the door frame gets abused and sometimes cracks. The whole thing could be moved down the door, but that would be ugly with unused slots/holes in the frame/door.
After looking and looking for a repair striker plate similar to this one:
I gave up and made my own.
It works with 1.25″ thick doors or thicker. Make you own from the DXF or I made a bunch and will send you one for $24 (my cost) + shipping.