Hold a gun to the head of the person using the browser.
Though, be aware that you aren't guaranteed of the required behaviour (in
which case, you'll have to pull the trigger).
There is no other possible way of preventing a user from closing a browser
window.

The rule, "Two negatives make a positive" was applied, and as such, the
excerpt from your problem statement "not not" was removed (due to
redundancy) during my evaluation of recommended advice.

Hope this helps :)