Can a supernova remnant have a habitable zone?

A habitable zone planet is defined as a planet within a proscribed distance from a star, not too close, not too far. Since the remnants of a supernova explosion means there isn’t a functioning star left, there isn’t a “Goldilocks” distance.

And, any planetary matter would probably be destroyed by the supernova explosion.

So short answer, no.

I suppose it would depend on the inhabitants of whatever planets were left. If things like extreme cold, radiation, and photosynthesis aren’t important for the plant life, or animals there, it could be a temporarily livable place. We know of at least one organism that can survive similar circumstances. Russia claims to have found alien bacteria on the exterior of their space station…

To me, short answer is possibly.

Sure they do. And you and I just happen to occupy the habital zone of ALL of them. Go figure.

The Earth, and all the heavy elements it contains, were ejected during a supernova event and so it is true to say we exist within the remnants of an ancient supernova.

And so the short answer for me is yes.