Before you go on and write such a system it's better to test if the LLM can do debugging to an efficacy level that we require. I don't think anyone has tried this yet and we do know LLMs have certain issues.
But make no mistake, the possibility that an LLM knows how to debug programs is actually quite high. If it can do this: https://www.engraved.blog/building-a-virtual-machine-inside/ it can likely debug a program, but I can't say definitively because I'm too lazy to try.