Bastien Dejean wrote:

  Every Java powered applets I browse to crashes X.
  I tested it in another WM (herbstluftwm), and it doesn't happen.

Then it's crashing the WM, not X.  The X server is exiting because the WM
exited.

You didn't say what you're using for session management.  I would look for
log files to see if openbox said anything before exiting.  I would also run
it in gdb to see if I can get a traceback but that's not easy if you don't
already know how.  But maybe you do if you're building from source.