Basically, the magnet stops being superconducting (or heats up too much, for quenches happening during charging), and it dumps its energy into the surrounding liquid helium keeping it cold, and thus, the helium instantly boils off, displacing the air in the room.
Quenches and other gaseous discharges (like a nitrogen tank boiling off) are dangerous because you can suffocate without even realizing it. Your body doesn't get the signal of high CO2 levels warning you of danger and you just pass out and die if you linger around it and there isn't enough ventilation or an O2 alarm.