Is there any way for me to look at the current running desktop through ssh? Meaning, if I ssh from machine A to machine B, I get terminal access in machine B. And if I run ssh -X from A to B, I can launch GUI programs. But is there any way for me to see the desktop as it appears on machine B? I have some processes running on machine B, and it isn't an option to kill them and start them again via ssh. (One of the processes is a GUI application, but the rest are running through terminal.)
Yes, there is a way. It's called Virtual Network Computing. You need to run a VNC server of your choice on the host machine(B), and you will need a client on your local machine(A).
There should be more options on both VNC server/clients but TigerVNC is an open source free option.