knaidlach:
Nice idea. However, the goniff that wants to steal but doesn’t actually take anything (because nothing was there to take) was not in violation of the issur to steal. By providing something, the generosity of the few dollars might be the issur of לפני עור לא תתן מכשול. I suspect a better option would be to have some means of surveillance, and to catch the thief. That way he/she could get the help they need, which is not the money (they might need that, too). but the therapy to learn to live a normal life.