Recently I've faced situation, when "standard" disk space monitoring failed - Zabbix uses vfs.fs.size item for checking disk usage, which is documented and preconfigured in bundled templates.
The Problem:
When files are deleted, but file descriptor/handle is still open - disk might be filled, but Zabbix will report no usage in this case.
How can one monitor disk space in this case?
Here is a test i've done :
I create a 600Mb file and open it with less :
Now df show that more space is used :
now if I remove my test file :
df says :
so the space is still in use, we can see it with lsof |grep deleted :
now if I stop less :
df show that the disk usage is free :
I think your problem comes more from a bad intepretation of df due to percent reserved for root.
From the last df, total minus used minus available equals :
So maybe your user has a disk full error, but root can still write to disk, and Zabbix will not see disk full due to percent reserved for root.
You can check and change this with tune2fs