What is this inductive component?
The device is in fact a solenoid, or specifically a solenoid door-latch or magnetic latch.

When the solenoid coil is energized, this causes the movable ferromagnetic metal piece to be pulled towards the solenoid core. This unlatches whatever door or moving part the device is affixed to, allowing said door to open.

A spring return will typically move the metal piece away from the core once power is removed from the coil. This allows the hook-like ending of the metal piece to latch in place the door etc, holding it closed until the coil is re-energized.