The chute of the F-16 comes also in a soft pack, holding the actual dragchute together with a smaller pilotchute on the "open" side of the pack.
The package is hold in the latch / hook mechanism by a big pin, approx. 1 - 1-1/4 " of thickness.
The chute is deployed electrical/mechanical by a pilot chute that comes out b a big spring of approx. 1 foot.
The spring is loaded and holded by a small pin that can be retracted when selecting chute in de flightdeck.
The airspeed takes the pilot chut along followed by the dragchute itself, just like a parachute.
When the chute had done its work, the pilot turns the aircraft with an angle on the runway / intersection and releases the whole soft pack, just by switching it on the flightdeck, this prevents the chute to burn on the (exhaust) nozzle.
The latch / hook unit you are showing on the picture looks a like, only the F-16 I know is approx 30+ years old...
The dragchute is a time limited part and has to be replaced on a regular interval.
I hope you can understand my English a little bit, nowadays I only give lessons in Dutch
