What's the use case specifically?

WHY do you need this. There may be another solution that by purely focussing on sessions is preventing you from seeing. Tell me what you're trying to achieve

I am using a third party application which terminates user session when browser is closed. Consequently, I need to ensure that my Next.js application also logs out the user in this scenario.

A few ideas:

0. Most likely they're storing the logged in session in memory and not with a session cookie, or some sort of session storage

1. Use window.onbeforeunload, this may work for your uses to trigger a logout

2. Session cookie is hashed using something that exists in memory or localstorage. Gross version of 0. above

3. They might use a use a live websocket, and closing the browser closes the connection