The Apollo LM had three independent propellant supplies: tankage in the descent stage usable by the descent engine, tankage in the ascent stage for the ascent engine, and in the ascent stage for the reaction control system (RCS) thrusters.
Prior to the initiation of descent and landing, only the RCS would be used, and very little of it.
During the descent, fuel quantity was carefully monitored. There was a low-level threshold (5% of total tankage) which would illuminate a fuel quantity light in the LM cabin; once that light came on, mission control started a 90-second countdown to a "bingo" call, meaning a fuel-critical state. At the "bingo" call, the mission rules specified that the LM had to touch down in the next 20 seconds or abort. This gave the final decision to the mission commander in the LM; if they were 50 feet from the surface and coming down smoothly at "bingo" they could go ahead and land. The abort mode in this case would involve going to full thrust on the descent engine (if there was significant fuel left), then staging and firing the ascent engine to return to a stable orbit. Touchdown at higher speed wasn't likely; if they couldn't land safely they'd abort.
Apollo 11 and 14 came closest to depleting the descent stage fuel; for 11, at touchdown there was 18 seconds left to "bingo", and probably 45-60 seconds of fuel actually remaining -- 770 lbs of fuel. The other landings had 1100+ lbs of fuel at touchdown.
I don't know if there were mission rules regarding the RCS fuel during descent; the gimbaled engine on the descent stage allowed most of the descent phase to be executed with very little use of the RCS.
The ascent trajectory was also computer-controlled, so there was relatively little variation in fuel usage until orbital insertion. Once in orbit, only the RCS would be used to maneuver the LM to rendezvous. It was possible to transfer remaining ascent fuel to the RCS tanks, and if, somehow, the RCS was completely depleted, the Command/Service Module (CSM) had its own RCS and could take over the active role in the rendezvous, and reach the LM.