Google's John Mueller said that in some cases, if your site goes down, Google may start to remove URLs from its index within two days. This is on a URL by URL basis, so Google needs to see if the URL is not active and then try a couple more times, and if it is still not coming up, Google can remove it from its index within two days.
John said this on Twitter "Depending on how it goes down, we can start dropping URLs after a couple of days. This happens on a per-URL basis. Also, when it comes back, often we can catch up quickly again too."
Here is that tweet:
Depending on how it goes down, we can start dropping URLs after a couple of days. This happens on a per-URL basis. Also, when it comes back, often we can catch up quickly again too.
— 🍌 John 🍌 (@JohnMu) March 30, 2020
This isn't really knew, Google has said this back in 2007 and Matt Cutts even posted advice on what to do if your site does go down back in 2013:
Forum discussion at Twitter.