For the Shuttle, the flight rules cover these cases.
The O2 and H2 tanks had quantity "redlines" defined - operation of the tank heaters below those quantities could cause the heaters to overheat. The redlines were 2.5 % in the H2 tanks, 6.5 % in the O2 tanks.
The 2.5 percent and 6.5 percent numbers are the minimum quantities
guaranteed to be obtainable prior to reaching maximum tank heater
When (if) you got down to those quantities, you stopped using the tank.
Other sections of the rule covered the case of losing supercriticality.
FOR SITUATIONS IN WHICH THE TANK PRESSURE GOES BELOW THE CRITICAL
PRESSURE BUT IS STILL ABOVE THE TWO-PHASE SATURATION PRESSURE, HEATERS
MAY BE USED (DUAL HEATERS ARE PREFERRED) TO RAISE THE PRESSURE BACK
ABOVE THE CRITICAL PRESSURE.
IF THE TANK PRESSURE FALLS BELOW THE TWO-PHASE SATURATION PRESSURE,
THE HEATERS WILL BE DISABLED UNTIL NORMAL HEAT TRANSFER INTO THE TANK
RAISES THE PRESSURE ABOVE THE TWO- PHASE SATURATION PRESSURE. THE
HEATERS MAY BE OPERATED ONLY IN A CONTINGENCY SITUATION.
Space Shuttle Flight Rules, Rule A9-258 and rationale
Apologies for the all-caps but that is how the rules were written. The first quote is rule rationale and therefore not in all-caps.
Here's a screen shot of an MCC cryo display about halfway through the STS-88 shuttle mission.
(Source: personal notes)
You can see that Tank(s) 5 have been depleted and are at their quantity redlines. Tank(s) 4 are in use and being depleted. Tank(s) 1 and 2 were used for ascent and early in the mission, Tank(s) 3 have hardly been used at all.
Note: Please keep in mind these supercritical fluids are reactants used in the Apollo and Shuttle electrical power systems. They are not propellants used in the propulsion systems.