Hello guys i was facing the same problem when I deployed my selenium war in linux server and after RnD find a solution for the same.
You have to simple follow these steps :
1. Install VNC its a chrome extension or any remote desktop software.
2. In which server you have deployed your application like i was using TomCat server ,So run the TomCat server after taking remote of your virtual server .
3. Now run the servlet from any client machine , Its done, Now you can close the virtual server window test cases will be running in server.
Here when we take remote of server so we are providing a complete desktop to the server and when we now run the test cases server executes them same as in desktop even we have closed remote window.
I hope you got my point.