I found a related post on StackOverflow proper that shows, the information about approvals is stored in sqlite3 database at
If you can find your kext in the
kext_policy table, then it has been approved. Here is an example:
SQLite version 3.19.3 2017-06-27 16:48:08
Enter ".help" for usage hints.
sqlite> select * from kext_policy;
4C6364ACXT|com.parallels.kext.hypervisor|1|Parallels International GmbH|1
4C6364ACXT|com.parallels.kext.vnic|1|Parallels International GmbH|1
4C6364ACXT|com.parallels.kext.netbridge|1|Parallels International GmbH|1
4C6364ACXT|com.parallels.kext.usbconnect|1|Parallels International GmbH|1
I needed this information in order to know why Parallels is suddenly asking for my approval again today, when as you can see it has clearly been granted already, but for my benefit the System Preferences isn't presenting me with any "Allow" button to grant it again. Perhaps Parallels is detecting that a new kext needs to be approved, but it seems Parallels hasn't actually tried to load it yet.
Unfortunately for me, since I was hoping I could remove the permission and get the "Allow" button back, the database is strictly read-only. The procedure for removing approvals involves booting with a recovery partition and sounds onerous. I guess I'll wait for Parallels support to answer via Twitter!
Credit for this answer goes to StackOverflow user @mikhail-iakhiaev https://stackoverflow.com/a/51684219/661659
(Edit: the issue was not with Parallels, my help desk admitted that our managed Mac workstations all got an update today that removed our ability to approve kexts as users. They hope to have it fixed by tomorrow, but for the benefit of your question, that's another avenue where your users might have ended up being stopped from approving your kexts as any other user would. Hope this helps!)