You can use Execution.GetStates and check the termination state to see if the execution is terminating. The default behavior of TestStand is for an execution to terminate when an error is encountered. If you want to know specifically that an error occurred and what that particular error is then you should pass RunState.SequenceError as a by reference parameter to your asynchronous sequence that contains your monitoring VI and then monitor the fields under that parameter (i.e. check MyParameter.SequenceError.Occurred to see if an error occurred).
Hope this helps,
-Doug
