You should regularly review your disks capacity and when disks are getting full you should take preventative measures to maintain service. To alert administrators of low disk space, an email notification is sent to the admin account. The default is to send out warning alerts when the threshold reaches 85% and a critical alert when the threshold reaches 95%.
When starting services with zmcontrol, if the threshold is exceeded, a warning is displayed before the services are started. You should clean up your disk to free up space.