So our heat pump (heater) wouldn't shut off last night. Even after resetting the thermostat. When we tried cycling the switch from hot to cold if refused to turn off still. I ended up having to cut the power to the furnace at the circuit breaker. I saw the sticky for checking if thermostat is broken but that was for if it refused to turn on. Our thermostat is a robert shaw 9620

When you turned the thermostat off, did the outdoor unit continue to run or just the indoor fan? You may have a heat relay with fused contacts, keeping the auxiliary heat powered.

Yea, the outdoor unit turns off but the fan in the ceiling stays on.

Does it blow warm or cool? If warm, sequencer or heat relay is stuck. If cool, fan relay is stuck.