They require extremely low cooling from the helium to achieve superconductivity.
And with superconductivity, by definition, current flows without resistance; it continues even without energy, so turning off the power won't stop it. Nor will it heat up and decay from resistance. Modern MRIs are well-insulated enough to maintain their field without power from days to weeks.
The only thing that collapses the field is to warm it up to where superconductivity stops, which can be done slow and expensively, or in an emergency, fast and even more expensively.
By venting the supercooled gases in what's called a quench, you can turn it off faster, but the time it needs can depend on the model. It could be 20 seconds, or it could be 2 minutes, which, depending on the emergency, may be insufficient.
A quench itself can be dangerous, though usually less so than a patient pinned to the magnet. There's a chance that poor ventilation can flood the room with helium, causing loss of consciousness in seconds. The increase in pressure can also make it impossible to escape if the door's not built for that. You'd have to break a window. On top of which, it's dangerously cold, and the explosive bang can rupture your eardrums.