Generally there is no guaranteed way to trap the closure of a web browser and certainly no way for PxPlus to handle or even be notified about it without you putting some code (JavaScript) in your web page to handle the issue.
Most browsers support an 'onbeforeunload' event where you can display a warning message if that is what you want.
You can also try trapping the 'onunload' event and have it send a Ajax style message to the server -- however at this point you cannot prevent the closure from happening.
Regardless of what you do you need to consider that the browser being closed may be due to circumstances beyond the control of the user or browser. Power failure, reboot, forced close, loss of connection, etc.. are all reasons that your browser connection may be terminated.
What I would suggest is you create some form of background polling between the browser and PxPlus where you can consider no polls for a period of time as a disconnect. This s what iNomads does in order to help assure the browser is still connected as well as setting an 'onbeforeunload' event handler.
As a side note, if you are looking to trap the browser closure so that you can 'save' information the user has entered you might consider using 'localStorage'. You could create some JavaScript to preserve user input, form information and state in Local storage. You could re-use this later when the browser was restarted and the user re-connected to the site. Perhaps by attaching to the onsubmit event you could save the data being submitted and target URL, then on reconnect re-submit the data. Good web logic should already be capable of handling re-submissions so you likely would have little to change on the host and merely have to create some JavaScript to attach to the <form>.