They are simple things, but they don't go critical like you're describing. Simple ones often just have a mechanical bimetal thermostat device that opens / close

They are simple things, but they don't go critical like you're describing. Simple ones often just have a mechanical bimetal thermostat device that opens / closes around a given temperature (a bit north of 100degC). In addition to that, they have thermal fuses that will blow if the temperature reaches over some threshold (I think 200degC?). My understanding is that they often use a pair of thermal fuses for safety. In this case, you would somehow need to have both thermal fuses fail closed, as well as the thermostat fail closed.