M. A has a single, international-to-domestic ticket.
They however get pulled into a further secondary inspection, which makes them miss their flight, but is ultimately admitted.
Does the airline have to accommodate and rebook or can they treat it as a delay of your fault and strand you?
They don't have to but in most cases they will. It depends a bit on the mood of the people on the ground and your negotiation skills.
I never went in secondary, but once I have huge immigration queue on US immigration border, so I missed the domestic flight.
I went to the gate, and staff told me they automatically rebooked me on the next flight. No need to discuss with them. I do not know if it was an airline policy, or if things have changed since them.
I think you should tell the staff about your next flight, so they can advice airline in time (but it will not work well on getting things quick). That queue seems never moving (from one person which had problem with fingerprint reader).
BTW it was around 10 years ago. For sure before COVID.
I would strongly recommend not counting on a rebooking or any guaranteed compensation of any kind. The likelihood of it happening would probably depend greatly on the airline's overall reputation for service in general. For instance, a poor-quality or cheap carrier I would expect would fight a rebooking as much as possible.
On the other end of the spectrum are carriers known for their good service. A personal experience is that a family member of mine always gets stopped at US Customs for secondary screening when arriving on Air New Zealand. Usually it's not a big issue, but this time we already had a short connection and a delay on the Air New Zealand flight, plus an Emirates A380 dumped their entire load of 500+ passengers in the Customs line at once.
Even some passengers who didn't get stopped (only delayed by the line) in Customs were missing their connections, so when we get to the rebooking counter the agent was automatically offering everyone a rebooking, plus a hotel stay and a very generous dinner and breakfast allowance. We ended up not being out any cost for the situation. I wouldn't have trusted United or American to do the same if the booking had been through them, and I'm sure Delta would offer the rebooking but might not offer a similar hotel/food compensation.
TLDR: If you're booking on an carrier known for poor service, you're probably not going to see any compensation. If you're booking on a carrier known for their good service (like AirNZ) and/or there's a delay involved, there's a good chance they'll be offering it without you even asking, especially if you're not the only person missing the connection. In our case there were at least 12 of us from multiple parties who missed connections from our flight.
Many non-US airlines explicitly disclaim liability for passenger delays due to security/immigration issues, and so will NOT re-book you for free unless you get an exceptionally nice handling staffer willing and able to bend the rules without risking their job.
