I would vote for 'start craving brains'. All that is intended as a joke, it captures what I think actually happens pretty closely.
'Mindless' is a bit of a misnomer. Mindless undead are mindless in the same way that windup toys, cockroaches, and computer programs are mindless. Just because they have no really thinking process doesn't mean that they can't produce complex behavior. When no longer controlled, mindless undead obey a heirarchy of goals.
1) Kill living sentient beings.
2) Move toward places of natural evil, and flee from places of natural good - provided that doing so does not prevent the immediate fulfillment of goal #1.
3) Follow the last order given, provided that doing so does not prevent the immediate fulfillment of goals #1 or #2.
Mindless uncontrolled undead try to fulfill the above goals mindlessly. That is to say they can't plan thier actions. They can only react to immediate stimulus.
Situation #1: A group of zombies are left in a tomb with the instruction 'Guard this place'. Those zombies latter go uncontrolled. So long as no living sentient beings come near, the zombies simply stay in place looking unanimated. The last instruction given them does not require them to violate any of thier higher goals, so anyone that comes near is attacked until dead. Once there are no living sentient beings around, they go back to following thier goal of 'guarding this place'.
Situation #2: A group of zombies are left in an open ordinary meadow with the instruction 'Guard this place'. Those zombies latter go uncontrolled. The moment the sun comes up, the meadow becomes a place of natural goodness and the zombies do thier best to leave it, moving randomly in various directions until they either come across living sentient beings, or they find a place of natural evil (or at least that's out of the sun).
Situation #3: A group of zombies are part of a work gang with the last instruction to move bags of dirt from one location to another as part of a large contruction project (say a levy). Those zombies latter go uncontrolled. The zombies now immediately turn on the human workers in the work gang and try to kill them. When no living sentient beings are left nearby, the zombies then 'notice' that the area that they are in is lit by sunlight. They go stumbling off in random directions trying to find a place of natural evil (or that's at least out of the sun). Eventually, if the sun goes down and some of them are still in the area, they return to trying to fulfill the last instruction given to them. Otherwise, they do nothing except await living sentient beings to come by for them to kill.
Note that this sort of behavior is one reason that the spell 'Animate Dead' qualifies as evil. No matter what the best intentions are of the person animating the undead, the undead themselves remain naturally evil creatures who will - as soon as they are no longer attended - revert to 'craving brains'.