That sounds like a contradiction in terms. How does a Mars colony survive event X? An isolated population in an engineered ecosystem on Earth survives X with higher probability.
I'll even make a positive case for Earth being safer: Out of events which could destroy even a physically isolated, rad-hardened population, all of the most probable would also eradicate life on Mars. The most probable of those are deliberate actions by a malevolent entity, such as in a hard-takeoff UAI scenario.
In such an event, your only hope for long-term survival is to hide, and hidden is one thing an offworld colony can never be.
Mars colony survives a mass dying in this hypothetical by not being the target planet of the mass dying.
Of course, you have threats that can impact both. Improvement by degrees is still beneficial though. Even though a backup is not useful for this type of risk, in the original hypothetical it is useful.
Also, of course you can switch the hypothetical around and consider Mars getting hit by the mass dying event. But we're talking about the value of having a backup and considering low likelihood situations where having that backup shows its existential benefit.
Eh, I feel like we're just talking past each other at this point. Just to clarify exactly what my position is:
We posit that it makes sense to have a "backup": A physically isolated, self-sufficient ecosystem in which human civilization might continue independently. We can decide to put this backup in a distant gravity well, and call it a "colony". Or, we could decide to put it somewhere very, very safe on Earth, and maybe call it a "bunker".
My stance is that bunkers are universally preferable to colonies, at least for the foreseeable future of human technology: the bunker survives the same extinction events that the colony survives, and the inhabitants of the bunker have a better shot at rebuilding afterwards.
Reading between the lines, you seem to be supposing some event which destroys the bunker by definition. That would certainly suck for humanity, but it's answered by my most recent post: If there are human-extinction events the (Earth+)bunker wouldn't survive, there are dramatically more such events the (Earth+)colony wouldn't survive. So existentially, on the balance of probabilities, you are better served by building bunkers rather than colonies.
Mind you, I'm not saying there's no point in a colony; at some point, if you already have a dozen or a hundred bunkers, the marginal utility justifies the expense. And of course there are lots of reasons, both practical and sentimental, why we might want to go to Mars. It's just x-risk ain't a very good one.
I'll even make a positive case for Earth being safer: Out of events which could destroy even a physically isolated, rad-hardened population, all of the most probable would also eradicate life on Mars. The most probable of those are deliberate actions by a malevolent entity, such as in a hard-takeoff UAI scenario.
In such an event, your only hope for long-term survival is to hide, and hidden is one thing an offworld colony can never be.