Is it negligent to depart with one thrust reverser inoperative?
No, it is not negligent.  Landing performance data assumes no thrust reverser usage and thrust reversers can be dispatched inoperative per the Minimum Equipment List (MEL) with a logbook entry and possibly the inoperative reverser mechanically locked/disabled.  With a single thrust reverse operative, depending on the aircraft and airline ops, the other one may or may not be used.  If it is used, caution in maintaining directional control during landing is advised.  Any such stipulations will be part of the MEL verbiage.

A proper MEL action will consist of a logbook entry by the pilots or maintenance, a logbook sign-off by maintenance and dispatch notification of the MEL.  Thus, the pilots, maintenance and dispatch are all aware of the issue.  Lastly, and special requirements of the MEL will be noted by the crew when they consult the MEL book after noticing the MEL in the logbook and in the dispatch paperwork.   In the airplane I am familiar with you could visually note the thrust reverser locking bolt during the walk-around inspection to verify that maintenance had done its job properly.  This also presented a nice opportunity to query the First Officer and see how well they were paying attention during the inspection.

The situation would only be negligent if proper procedures were ignored.