In OS X there's a separate pasteboard, NSFindPboard, used to keep search fields in sync. The pasteboard gets updated when a search field changes or the user hits ⌘-E with text selected. It can be pretty handy when you're searching through code for the same keyword, and most apps seem to generally respect it (Safari/XCode/Chrome/etc). In general it seems like apps check it when they become active and update their search fields.

Chromium definitely supports NSFindPboard (with some of the impl here), but I'm not sure that stuff is accessible at all from the Javascript layer.

One option is just to shell out to pbpaste/pbcopy to get/update the pboard's contents, as in:

 pbpaste -pboard find

will dump the contents of NSFindPboard to stdout.

You could also technically get at it with NodeObjC, but that seems like overkill.