The SSME (like all modern, high performance rocket engines) is a big
turbopump. Big turbines, run from the same fuel source as is being
ignited for use as a rocket. If the turbine is cranking away at full
power and the source of fuel suddenly goes dry, then all that power
being put into maintaining revs suddenly gets put into turbine speed.
Depending on if you're lucky or not, the engine will detect this and
shut off the turbine before it goes dry or before it overspeeds
destructively.

I wonder if these low-fuel sensors are part of the system that shuts
down the SSMEs if there's a fuel starvation issue. I remember a
mission a few years back where MECO (main engine cut-off) was
unexpectedly a few seconds early because of higher then projected fuel
burn or something. Not enough to really impact the mission, but it
showed the safety systems that prevent dry-running SSMEs was working.

Ben Hallert
PP-ASEL and space nut