Why would there be a cord to get rid of an unopened parachute?
On modern parachutes it won't actually get rid of an unopened main parachute. A main parachute that refuses to open at all is actually scarier than a poorly opened one, because it could get open anytime. Including after you have opened the reserve one. Then you have two parachutes open, and they can get into surprising unstable aerodynamic configurations (a downplane). And you can't easily get rid of an unopened main parachute.
Source: I learned skydiving this summer