Overspeed protection is just physically protecting the actual moving parts (N1/N2) from going too fast. For this you get EICAS ENG RPM LIMITED (L/R) and the EEC's will simply limit N1/N2 from going too fast, there will be no immediate shutdown/idle or any previous rubbish you have been told by lomapaseo.
From the Boeing Maintenance Manual regarding the RR
Trent Engine:
"If the engine N1, N2 or N3 speed goes to the redline, the EEC modulates the fuel flow. This prevents the engine from exceeding the N1, N2, and N3 redlines.
The EEC (also) monitors the LP turbine for an overspeed condition. If the low pressure shaft breaks, the EEC closes the HP fuel shutoff valve.
Overspeed Protection Unit (OPU)
The OPU prevents a LP or IP shaft overspeed. The OPU monitors the N1 and N2 shaft speed sensors. If an FMU failure causes an overspeed condition, the OPU supplies a signal to the FMU that closes the HP fuel shutoff valve."
The manual adds that the OPU shutdown occurs at about 10% above redline.
I recall that US regulations imposed additional restrictions on RR engines for overspeed. There was also an overspeed shutdown on the 747-400's RB211.
One man's rubbish is another man's truth
Rgds
NSEU
(Edited for typos)