jargon said

On a Mac with OS X 10.6.8, Firefox version 48 from Aug 2016 is noted as the last version to support this OS version--version 49 will not support OS X 10.6. But what about updates to version 48, such as update 48.0.2 issued in Sept? Should I try to install it on my OS X 10.6 system?

By 48 version it is all so 48.0, 48.0.1, 48.0.2. The Firefox 48 is EOL now that Firefox 49.0 is Released.

The only option Mac OSX users using 10.6, 10.7, 10.8 have in getting security updates with Firefox is by using Firefox 45 ESR. It is basically based on the 45.0 Release but with most of the security updates the latest Release gets. The last update will likely be 45.8.0esr which will come out at same time as when Firefox 53.0 is Released unless Mozilla extends support of Firefox 45 ESR as there are normally eight updates not counting the minor.

https://www.mozilla.org/firefox/organizations/faq/ https://support.mozilla.org/kb/firefox-osx

This did not answer the question. Is update 48.0.2 supported on OS X 10.6? Or will update 48.0.2 break Firefox on OS X 10.6? (At this time, Firefox v 48.0.1 is working fine on my 10.6 system.)

Well I did answer the question in that when it says Firefox 48 is the last to run on OSX 10.6, 10.7, 10.8 it was referring to 48.0 and the minor updates 48.0.1, 48.0.2. The Firefox 48.0.2 was released for Windows users in mind to try and fix a startup crash though. I also answered if Firefox 48 was still supported and it is not as it was made EOL (End of Life) when Firefox 49.0 was released.

Firefox 48.0.1 will get behind on security fixes and more vulnerable as time goes on so your only option to be more secure with Firefox is to use the Firefox 45 ESR as I mentioned.