I am trying to setup Websocket based PHP chat application from Chat-Using-WebSocket-and-PHP-Socket on Bluehost on domain XYZ.ABC.com.
I have changed $host to XYZ.ABC
If you have shell access you need to run the script with
nohup <command> &
It will then run in background and not stop if you leave the shell.
If you don't have SSH access there is no chance in keeping it alive. Look for a cheap vserver or rootserver with SSH access then.