Oh yes, it definitely happens.
Websites may seem to be carved in stone, but there are a lot of moving parts under the hood. Software upgrades, viruses, disgruntled employees, lost passwords, hosting company errors, and a host of other reasons can cause your site to become unusable and even go off the air.
I have rescued many websites from such problems. There are cases where there is no remedy, but often, we can find a way to resurrect a website that has issues.
I am a stickler for making backups. All my client sites are backed up DAILY for the last 30 days and I save monthly backups for the last 6 months. Rarely does it happen that we need these backups, but when we do, they are a total blessing!