Our shower stall sits on a concrete slab, typical of 40 yr. old Hawaii houses. It is tiled. I have just noticed that the grout on the bath and hallway tile looks wet. The shower sits between. It is coming from the plumbing wall. The inside base has been caulked and I can't find any cracks. A friend told me these stalls are lined with some kind of felt paper that has probably cracked at the base. Is there a quick fix since we will be moving in a year and don't want to replace the entire shower.

If the liner has been ruptured or pulled away from the drain body, then there really is no quick fix that I'm aware of.

Since it is coming from the plumbing wall have you checked the shower arm to see if it is leaking. The arm that comes out of the wall will be threaded on both ends, one is the shower head end, and the other end will be threaded into a elbow. That could be your problem. Also have you checked the plumbing lines, hot, cold, and riser pipes. You could also have a pin hole in your riser pipe. Do you have a access panel to the plumbing? If so run the shower and check for spray coming from the pipes.

You may also want to call RE-BATH, they may be able to put a liner over the shower stall, and the walls, this may help when you go to sell your home, I hear they have a preaty good system, and warranty.

Isolate and eliminate.
To satisfy your mind about a pan failure and avoid disclosure problems when you sell, do a pan test. Remove the strainer from the shower and get a wash rag, wet it and put it in a plastic baggy. Stuff it down the shower drain just enough to stop water from draining. Get water in a bucket from a source other than this fixture and fill the shower with at least 1 1/2" of water. Wait 30 minutes. If no water appears to be leaking the pan has not failed.
The next test would be to fill buckets from the shower but do not let it drain. This would test the shower valve and shower riser.

isolate and eliminate.
to satisfy your mind about a pan failure and avoid disclosure problems when you sell, do a pan test. remove the strainer from the shower and get a wash rag, wet it and put it in a plastic baggy. stuff it down the shower drain just enough to stop water from draining. get water in a bucket from a source other than this fixture and fill the shower with at least 1 1/2" of water. wait 30 minutes. if no water appears to be leaking the pan has not failed.
the next test would be to fill buckets from the shower but do not let it drain. this would test the shower valve and shower riser.

Bravo doug238
Excellent answer.
Syrell