What happens when a nail comes off?

Depends a bit on why it came off.

If the growth zone of the nail (slightly behind the cuticle) is basically OK, the nail will grow back, but it can take almost a full year before it's reached normal size and shape again.

If the growth zone is damaged, then the nail might come back deformed.

Thicker, cloudy, wavy or anything like that.

It may eventually return to normal, or it may always be strange.

If the growth zone is really badly damaged, or actually missing, the nail might not come back at all.