A damage can simply be the everything. If a strong concussion with a burst occurs, that means now you're with god. Turbofan engines do have 2-4-6 fuel flow entries, if one of them fails, the engine will be shut down and as seen as a complete failure on EICAS/ECAM. It is like a fuse that prevents a engine fire.
But, damages which can be varied, including turbines, wear/tears, outer high pressure area, electrical busbars etc. Anti ice is a part of the Electrical Circulation in Airbus as far as I know, so any kind of electrical failure also has a potential to mess up Anti-Ice.