It seems that it is a Linux Kernel bug what is described here:
Bug #1579135 “AppArmor profile reloading causes an intermittent ...” : Bugs : linux package : Ubuntu
and it has nothing to do with Plesk.
Plesk support was very helpful for to investigate this, THANKS, guys!
It seems that this Linux kernel bug is affecting some server systems. Not all of it. We do have four servers, all the same, software configuration, the hardware isn't the same. On two the problem occurs last week Tuesday in the night by automatic update routine, afterwards the server crashes. By rebooting, the server works nominal but Plesk was showing in the Plesk server config page errors, updates weren't done.
Next day same problem without server crash, then the next day server crash and so on. I started to find out the problem, but it takes me up to this week Monday to find out that I am not the only idiot who has this problem. At the moment I have disabled all automatic updates, Plesk and Ubuntu because it doesn't support any software installation without crashing the server.
I do think that you have the same problem like we do,
The suggestion I got is to update the Kernel version. I did the update on one of our servers, but I am not able to tell at the moment any result because I have to work now in step by step plan to find out if this error isn't there anymore. The update process was done perfectly. I do not have access to the server where I did the update at the moment, but this isn't a result of the upgrade itself, connectivity problems at hosters side. Happens then when it isn't needed.
Here you can read about the error scenario:
https://bugs.launchpad.net/ubuntu/+source/apparmor/+bug/1614459
It is precisely reproducing what is happening at the server systems at our side.
So far, the suggestion is to upgrade the Linux kernel. This bug was fixed in the Ubuntu kernel 4.4.0-38.57.
Will be back with results from our side.