Do PE rejections ever get reviewed and changed?

Let me just preface this by saying I know this is heavy copium on the back of a fresh rejection but I've seen a case where a SA was not given a return offer at the end of the summer, but months down the line because of headcount issues they were given an offer to join the team. So I am not pulling out of my ass, and genuinely wondering if anyone ever heard any stories.

But has anybody ever experienced in the first round, being rejected and HH says they decided to move on with better candidates, but they didn't get enough responses so they overturn a rejection and continue with candidacy? Again, heavy copium from a first year going through off-cycle but would be open to hearing some amusing stories.