PRs don't have expiration dates per se, but if a PR isn't being updated by the author and it can't get merged in its current state, it will be closed sooner or later. Often nothing happens after that, but sometimes (especially when it's an important PR or it's close to being done) other developers make a new PR based on it, like in these cases:
https://github.com/dolphin-emu/dolphin/pull/2517
https://github.com/dolphin-emu/dolphin/pull/3139
https://github.com/dolphin-emu/dolphin/pull/2517
https://github.com/dolphin-emu/dolphin/pull/3139