One could use the serial port to debug this, it should keep going even as the system fails. Lots of things could be wrong.
What version of L4T is it running? They ship with R19.2, the latest is R21.4…several graphics display issues of the earlier R21.x series were fixed around R21.3.
Heat is a possibility as well, does the fan run?
If running on an unsecured network with no firewall or router to block incoming logins, it could even be something on the outside causing this (ubuntu login password is standardized, the entire world knows what it is unless changed).
FYI, the borders of the apps are part of the window manager, which makes sense if it is graphics chip overheating or a simple X11 crash.
What is really needed is to have that serial port console connected and see what it says. The DB9 connector uses 115200 8N1 settings and should show details even as the system fails (serial port does not require any kind of networking or graphics, its just too simple to fail except under extreme conditions). If your desktop host does not have a serial port, you can use something like a serial USB UART to do the job (in conjunction with something like minicom or gtkterm):
If you have a lot of time you could clone the Jetson and look through the log files, but the serial port is faster. Here’s info on cloning…the root file system can be loopback mounted and inspected: