Air carrier Captain reported a passenger accidentally dropped a cell phone through the cabin sidewall while deplaning at destination. Crews were unable to retrieve the phone and the flight departed.

Narrative

While passengers disembarked on the inbound leg prior to this flight a passenger dropped her phone through the outer sidewall adjacent to the seat. Maintenance was notified and write-up sent. The boarding was delayed while technicians tried to retrieve the phone from the cabin side; but were unsuccessful. While boarding resumed; technicians continued the hunt by removing panels in the cargo compartment underneath the approximate location of the seat; but still did not find the phone. Calling the phone number sent us straight to voicemail; so a ring was not audible. Panels in cargo area were resealed and item was deferred. The entire crew had difficulty accepting whether this was safe to continue with deferral. I spoke with local Maintenance; who assured me that it was a risk assessed part of their procedure and they were good with the deferral. I phoned the Chief Pilot; who relayed a personal story of her own device getting lost and unrecoverable on a flight; that 'flew all over the system ... it happens all the time.' Her device when finally recovered was bent. The FO and I both inspected the cargo area to see if there were any potential ducts or parts that may aggravate the situation; but none are visible with the sidewalls resealed. I was able to find references for fighting a thermal runaway fire in the FOM; and a warning that 'batteries may explode or burst into flames without warning.' Also; Flight Manual (FM) relayed that the Thermal Containment Bag (TCB) was deferrable; but nothing about a lost battery/phone. The crew was conflicted that batteries were not allowed in checked luggage; they must be with the passenger; so the thermal runaway can be dealt with if needed. But in the case of a lost phone in the same location... deferred? I accepted the aircraft for flight and overrode the crew's concerns but was hesitant in my decision; which caused a considerable amount of angst among the crew. For myself; it also did not seem consistent that I would have to acknowledge receipt of paperwork; Dangerous Goods Summary; for Class 7 radioactive material in the cargo area so small the weight was not shown; but a known lithium cell trapped with unknown condition was acceptable.