Steve Bailey has suggested a workable solution, but in answer to your post, it is not possible for CompactLogix to turn an output ON if the processor faults. If the processor faults, or communication with the controller is lost, then the output modules will turn all outputs OFF
ControlLogix output modules have the option to turn OFF, retain last state, or turn ON, for each output channel, but not CompactLogix output modules.
The given approach seems to be the best solution - hold some outputs true with an unconditional rung, and if the processor faults the relays will drop out. Use the n/c contacts on the relays to drive the "outputs" that must come on. When the processor restarts, the relays will be energised again, and the n/c contacts will open.