Going past the 12 years is not the same thing (in risk terms) as going past 2000 hours.
There is nothing in an engine which is strictly "lifed" in an engineering sense. There are oil seals which won't last 100 years, of course, but if you have oil pouring out that will be kind of obvious... But most of the highly stressed parts are steel and steel does not have (AIUI) a fatigue life (aluminium has). Conrods for example will run "for ever" unless there is an inherent defect to start with.
For an engine to reach 12 years before reaching 2k hrs it would need to be doing 166 hours/year, which is about 5x the PPL average, and is more than I have ever done (max was about 140 I think, pure airborne time). There is no safety data suggesting that going slightly past the 12 years is a problem, on the old piston engines. The question is ... how far past?
I think most people would be suprised at just how knackered an engine is allowed to be before it is rendered unairworthy. I don't recall the Lyco oil usage limits but they are about 5x higher than what a normal engine should be consuming; on a long trip you will be carrying a boot load of oil bottles
Similarly with compression figures.