In superconducting magnets, this sudden loss of superconductivity is called a quench[1] and can be destructive. The LHC recently suffered from this, discussed here[2], and is undergoing repairs.

[1]: https://en.wikipedia.org/wiki/Superconducting_magnet#Magnet_...

[2]: https://news.ycombinator.com/item?id=36811018