Gangway connection

A British Railways Mark 1 coach fitted with a gangway connection of the Pullman type
Internal view of gangways between a British Rail Class 153 and a British Rail Class 158. Notice the doors on the sides, which prevent passengers from accessing the cabs of either unit. When the gangway is not in use, they lock outwards to block off the entire cab/gangway compartment.
View along full length of a Toronto Rocket, folding seats at the right

A gangway connection (or, more loosely, a corridor connection) is a flexible connector fitted to the end of a railway coach, enabling passengers to move between coaches without danger of falling from the train.