As an example the RB211-524G/H can shut itself down for a LP overspeed and can be reset by selecting the fuel control switch to off/on, this is an extreme situation though as it should prevent an overspeed prior to this by limiting the fuel flow.
Here's an bit out of the MM regarding the inspection required after an overspeed, you must first go to a graph which has time against N1,N2 or N3% which basically gives you three choices A) No inspection required, B) Inspect IAW MM........ and C) Reject engine.
Turn the IP system and make an inspection of the stage 1 compressor blades for this damage:
1)Cracks and tears
2)Nicks and dents
3)Tip failures, bends and rubs
4)Material which is gone from the leading or trailing edge.
Damage accept/reject standards for the IP compressor rotor blades
(a)Dents are permitted.
(b)Nicks and tears are permitted in the two edges of the blade, the length of each nick and tear must not be more than 0.015 inch (0.4 mm).
(c)Bends or curls in zone C are permitted.
(d)Blades with a trailing or leading edge tip broken off are permitted if not more than 30% of the blade chord width is missing, if subsequent stages of the blade are examined.
(e)Changes in the blade colour related to heat caused by tip rub is permitted.
(f)Burrs on the blade trailing edge tips are permitted if not more than 25% of the blade chord width.
(g)Cracks or nicks and/or tears less than 0.015 inch (0.4 mm) are permitted.
(h)Cracks or nicks and/or tears longer than 0.015 inch (0.4 mm) are permitted if inspected at regular times not more than 300 hours apart, with the standards that follow:
1)If the damage does not increase (no more deterioration is apparent) after three inspections, you may continue-in-service and do one more inspection after 1000 hours.
a)If after the forth inspection the blade condition has not changed, subsequent inspections are at the operators discretion.
This is just a few chapters there are pages and pages for this inspection so you can get an idea of how thorough it is.