Many messages like these are sent to Plesk administrator's email:
Plesk server is out of disk space:
# df -h
Filesystem Size Used Avail Use% Mounted on
/dev/ploop12525p1 9.8G 9.8G 0G 100% /
none 512M 4.0K 512M 1% /dev
none 512M 0 512M 0% /dev/shm
Free up some disk space (for example, clean up temporary files: How to clean temporary Plesk files on a Linux server) or extend the partition.
Note: managing disk partitions is an administrative task - please contact your hosting provider for further assistance.