Databases all use some kind of write-ahead logging so you'll be safe as long as that file is safe, and they're even capable of recovering the file all the way up to any corrupt records that may have been appended at the end.

You shouldn't use multiple servers writing to the same volume for database drives, but other than that it's no different than any other disk that might lose connection. Most VMs "local" disks are still attached over the network anyway, emulating a PCIe bus interface instead of NFS.