It seems like he noticed it soon (but too long) afterwards.Agreed, I'd have one team member stay put in case the cab comes back and have the other team member contact the cab company (provided they remembered it) and hope it turns up quickly.
Running the Race without passports was a short-term option to complete the leg, but having no money made even that very difficult.
When I traveled overseas, my passport and important ID documents were always with me on my person and tucked away where pickpocketing it would be very difficult. (Or in the hotel room safe, if I really didn't need to be carrying it around.) I'd never put it in my pack or a loose pouch.