Question: Suppose you have a PHP script that (for whatever reason) takes several minutes to run. If the user closes the browser while the script is running, does the script stop running, or does it execute instructions up to the end of the script?

Answer: 
PHP is a server-side language. All processing is done on the server, not in the client. Once the request is sent to the server, the client loses control over it.

This means that the server's configuration on timing out will come into effect on such long queries, but closing your browser will have no effect.

If you have used client-side (such as javascript) to submit multiple requests to the server-side language over a 5 minute time period, then yes, closing the browser will in fact interupt that process and prevent it from completing.

A good read about the differences if you wanted to read it:
<https://softwareengineering.stackexchange.com/questions/171203/what-are-the-differences-between-server-side-and-client-side-programming>
There's not a reliable way for the server to know that the client no longer cares about the request. In general, it will keep running until something stops it.