In the previous post Filling up NTFS partition forever without admin privileges I described the method to fill all free space on an NTFS partition without administrator privileges and without creating any large suspicious files. However, "forever" in the title was too strong a word, so I continued to search for solutions to cleanup the clogged $Secure file. Finally, I found this can be done quite simply: you need to use the standard Windows CHKDSK utility! I would've never thought that it had such a feature. Apparently, it was added in around 2009 in the KB919241 update.
So, just run chkdsk with the /f key and agree to reboot the system, or run it with the /sdcleanup key, specifically designed for cleaning unnecessary security descriptors (and also reboot the system). After rebooting and chkdsk execution, all unused descriptors from $Secure will be deleted. Of course, an inexperienced user is unlikely to guess the solution to the problem (after all, even understanding where the free space went is not so simple). In addition, running chkdsk requires administrator privileges, but the described method of filling up the partition does not. If a user with limited rights does not have access to the administrator account for some reason, the user will not be able to solve the problem on his/her own. However, the problem is not as serious as it seemed initially!
Finally here's the link to full documentation on CHKDSK keys.