We had a major earthquake in Kaikoura, New Zealand back in 2016. We had a group of Chinese guests staying at our holiday house there.
Fortunately our house only suffered light cosmetic damage, although there were houses that were destroyed or badly damaged, and there was one fatality. Power & water was out, and it was of course stressful with constant after-shocks coming through. From memory the roads were completely cut off for about a month. The navy sent in a ship & transported many of the tourists out after a number of days.
In our case, the staying longer issue wasn’t there because the Chinese government chartered helicopters and evacuated all Chinese nationals pretty much the next day. They were the first out of the area. I don’t think I would have charged for additional days, but then I didn’t really think about it!
Our guests were full of praise for our neighbours (who are our cleaners), for helping them, showing them where to find the torches, how to use the BBQ etc.
The biggest impact for me was giving subsequent guests the option to cancel, or wait and see how the access issues worked out. AirBnB were very cooperative & helpful in that respect.