Residence permit cancellation? Grace period?

I'm breaking contract with my current employer, and I've been told they will cancel my residence permit, but honestly it seems they have no idea what they're talking about. Can they cancel mu residence permit if I'm no longer working in China?

Follow-up: if it is cancelled, is there a grace period for me to leave the country, or am I expected to leave immediately. Say my last day of work is on the 12th and my employer puts in for cancellation that day..will I need to leave on the 13th?? Please help, I'm very confused and have no reliable source for this information.