believe it or not, but it happens a lot really.
2 classic cases :
- logs on an SQL serveur. to clear the logs you have to merge the logs with the main DB file.
- snapshots on a Virtual Machine. It creates two files than needs to be merged eventually.
Those merging operations needs twice the space as the separate files. The process can start but if there is not enough space, it would fail and all the files would be corrupt. You need space to restore the backup but at this point there is any. it's a catch 22.
Restoring a backup needs space wich is a problem if the backup is on the same disk as it was the case here.
Also, by default, Microsoft SQL server stores it's files on the system partition. So if the company maintaning it didn't payed attention, the problem would be even worse, the OS would crash.