The fan motor has a permanently-on live feed. Switching is achieved via relays on the earth side. A sticking-on or faulty relay will certainly cause the fan to run without the ignition being on. Your description of events suggest this is the likely cause. Of course, the relay may be activated through a fault in the control side. To 'stick on', the relay has to be activated first. Swapping with a new one should give you a clue.
TC
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