What happens when the server is in an infinite loop and the client stops?

The client (browser) has a TCP/IP session established with your server, waiting for the HTTP response of your website. When the user hits back/cancel/close, this TCP connection is closed immediately by the client.

The webserver (i.e. apache) will inform the PHP interpreter of the TCP connection close.

Unless the php.ini directive ignore_user_abort is set to 1 (on server side, 0 is PHP default), the PHP interpreter will then abort script execution when the current atomic operation finishes (in your example: echo())

However, even when you set ignore_user_abort explicitly to 1 you will hit PHPs max_execution_time or the apache TimeOut (both are configurable on server side, too)

also see ignore_user_abort() and set_time_limit()