As long as the aircraft is in private use, engine can run "on condition" for as long as engineers agree it is good. Once you wish to hire out, or use commercially in any way then lifed limits kick in. My O-360A4M is officially lifed to 2000 hours or 12 years. But I've only done 700 hours in 8 years, and although I'm now flying more (about 120 hours p.a.) I expect the time limit to runout before the hours, and because it's private I'll continue "on condition" providing still good.
Lycoming have recently stated that TBOs can be extended by multiples of 200 hours, but this is dependant on very regular use (I think they quoted 40 hours per month - so probably only helps flying schools).