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when you break a ground loop everything is still grounded!
But the earth loop impedance may be higher than planned, which does a couple of things. First, it means a fault from live to the casework will expose the user to a higher potential, and second the fault current will be reduced so protective devices (fuse, circuit breaker) will open slower or maybe not at all.
TL;DR: Never cut the earth connection where it is part of a mains voltage circuit.
gbj_tester
Removing ground from something isn't advisable but doesn't mean something bad will definitely happen. Ground is there more as a safety measure. Removing ground to check if that is the source of an issue, if done carefully, can be hardly labelled as dangerous.
If by removing the ground the hum is gone, that solves the issue and kind of proves there was a ground loop. Btw when you break a ground loop everything is still grounded!