Is there any way you can force a browser

No. "Force" isn't something that's appropriate on the web. "The other side", that is, the browser and the user, do as they damn well please. If they don't want to send a piece of information, then it ain't going to happen.

I've got a script in which I want to use it, but I don't want it to fail because REMOTE_USER hasn't been sent.

Then code around it.

Abigail