Try adding a hidden field to the details page and any other page that you expect the users to navigate to. Then store the value using this hidden field (may need to find a js function that gets called when leaving the page). If I'm not mistaken, these values should carry over.
I don't think you can attach events to the controls inside the browse controls. Never tried it. Could be why most of our screens make the browse control readonly, and then have the controls for the individual fields outside so that it acts like a form with an add/update/remove action buttons.