Apple fixes El Capitan kernel issue in supplemental security update
Apple on Tuesday issued a supplemental security update for OS X 10.11.6, fixing a kernel issue for El Capitan users that causes affected Macs to 'occasionally become unresponsive.'

Available from the Mac App Store , as well as through Apple's support pages, the supplemental update is a free download weighing in at 623.9 megabytes, and can be used by any Mac running OS X 10.11.6 El Capitan with Security Update 2016-003 installed. Security Update 2016-003, originally released in December, has been reissued at the same time and measures 717 megabytes in size.
Aside from the kernel panic issue, little else is known about the contents of the update. Apple is expected to provide more details after it updates the official security updates page.
Users of macOS Sierra are still waiting for Apple to release the next update for the operating system, with the fourth and latest beta released last week.

Available from the Mac App Store , as well as through Apple's support pages, the supplemental update is a free download weighing in at 623.9 megabytes, and can be used by any Mac running OS X 10.11.6 El Capitan with Security Update 2016-003 installed. Security Update 2016-003, originally released in December, has been reissued at the same time and measures 717 megabytes in size.
Aside from the kernel panic issue, little else is known about the contents of the update. Apple is expected to provide more details after it updates the official security updates page.
Users of macOS Sierra are still waiting for Apple to release the next update for the operating system, with the fourth and latest beta released last week.
Comments
Not sure if this is the same issue.
I have been having issues on my 2008 24" iMac.
A workhorse all these years but the last 6 months, it locks up shortly after boot up.
Not my primary machine but still a useful machine.
If this works, after a few months of use to verify, I will then install Sierra on it.
I'm in the 'been having problems' with hangs in El Cap. I resorted to wiping the disk and re-installing from the latest backup because I couldn't even restart the existing installation. I assumed it was a problem with my drive but maybe not. I'm installing the patch now. Wish me luck and I hope the rest of you are lucky too!
There exists the good work of two gentlemen, that created a workaround to install Sirera
WITHOUT Issue, on an entire range of "unsupported" Apple computers.
I have been running Sierra, including all subsequent updates through the Apple Store, without issue.
I even installed a supported wireless card, in my 2009 Mac Mini for 100%, full, wireless functionality.
Check it out:
http://forums.macrumors.com/threads/macos-10-12-sierra-unsupported-macs-thread.1977128/
and the actual tools:
http://dosdude1.com/sierrapatch.html