Just thinking aloud ... It is possible for a star to grow so large it collapses under it's own gravity. Along a parallel path (so to speak) when a conductor carries a current too large for it to sustain, it burns out.
Can a ferromagnetic object be imparted a field too strong for it? What happens then?
I would begin to guess the dipoles within the magnet can only be magnetized so far; a stronger field wouldn't have an effect. But surely the same argument could have applied to a wire conductor?