For an incandescant lamp, Hakutsuru has it right. All local outputs should turn off when the processor fails...there are exceptions, but usually not in the local rack.
For an HMI indicator, you can read the first five bits of S:1 in a SLC to determine the processor status. I don't have the bit patterns handy, but there are many possible modes: RUN, Remote RUN, Program, Test. You should look at the channel status for the channel you are communicating with too. If S:1/00 through S:1/04 are in the correct state AND the comms channel is healthy, you can report that as a "Program Running" condition on the HMI...