Many of these stats use pretty small relays which can become welded contacts, and some use solid state devices like transistors or SCRs and those can fail
One time a service call, complaint was "no cooling." This was a one time customer and we had not installed the system so I was unfamiliar. Before I entered the office building, I checked the 5 OD units and was unsure, because not all were necessarily "calling." But one the suction line was VERY VERY warm, and it was not a heat pump!!! Turns out the office people had bought a bunch of cheap import "setback" stats and one had failed, bring BOTH heat AND cooling on at once!!! The furnace was heating and the AC was "trying" to cool!!! LOLOLOL