You can never let that DEF tank run empty, the computer will stop the engine before that. And being low or empty has nothing to do with the DPF filter and the problems that you will have. That filter "loading up" will put the diesel into "regen" mode, which increases heat in the "one box" upwards of 1000 degrees, yes 1000 to burn the carbon and soot from the filter. A lot of idling and/or low RPM driving and starting and stopping will be the primary cause of DPF issues. Oh yeah, and DEF is basically ammonia made from cow piss. Good luck.
PS I don't even want to get into when the ECM "derates" your engine because the after treatment isn't functioning properly.