What can I use to back a door jamb strike plate with no framing behind?
I know of nothing short of installing something in the wall behind that frame - and oddly your door jamb does not have a stud there for the frame to mount to, as far as I know this has been common for a LONG LONG time.

From a security standpoint sounds like even the old system was there to keep honest weaklings from going rogue. 

So you can remove that Jamb and install some framing stud in the back of it , use screws to attach it how you need to so you do not need to cut your wall, other wise you will need to cut that wall to fit and there are a couple options here - cut only at the top and bottom and remove the jamb or cut a piece all the way down and install the stud.