Indeed. As I said,we've always had more than one (currently four, albeit one is often empty and switched off) - so a good few over the decades, and I think only about four or five of them have truly 'failed' - but, yes, a couple were as you describe, still 'running' (continuously, except when compressor over-heating caused a temporary 'shut down'), but without cooling adequately - but both those events were detected by my 'over-temp' alarms, which are trigged by a rise in temp of about 3-4 degrees above what it should be.Of the 7 or 8 freezers I've had anything to do with only 2 have failed and both were still running but not cooling sufficiently (and both were full for Christmas) allowing us to use everything well before near to going off ...
Kind Regards, John