This is a very interesting question. The advent of regional airlines, wholly owned subsidiaries, fee-for-departure carriers, etc. does create a conundrum that those pilots should definitely be discussing with their respective MECs and leaders.
A little historical perspective would also be helpful; what happened to the regional feeders during the UA or the NW strikes? (I know the structure was nothing like today, just looking for perspective/info)

In the past, there would be a 'snapshot' taken of the DL operation/route structure the day we walked. Anyone who flew (provided a service for DL or flew a DL route not previously flown by their carrier) would be considered to be 'flying struck work'.

Endeavor, even though they are wholly owned, fly their own schedule (determined by DL each month/week/day/hour). I would imagine that, if we were to be released and called for a 'removal of service' (strike), there would be a snapshot taken of the entire DL system. Since the FFD/WO carriers are not on strike and have their flight schedules set, as long as their managements don't add additional routes/frequencies than at the snapshot, they would be allowed to continue with their schedules.

The big question is 'to what purpose?' They fly their flights from the -burg/-ville's to the hubs but the passengers have no flights with which to connect.

For the FFD carriers that earn their money from DL based on flying their schedule, they still must be paid based on their contracts. The WO is the big question. How does Endeavor get compensated; based on flight segment or 'on a budget'?

I would imagine that the Endeavor pilots could continue to fly their schedule during a DL strike as long as it was the schedule that was in place at the time we went on strike. Any additional segments/frequencies would immediately be flagged by DALPA/ALPA National as 'struck work'.