[WoZeR]

That should allow you to parent the parachute to the player. If the player dies the parachute will die with the player and be removed since it is parented. If you remove the parachute everything will be fine.

I used that code above to parent TF2 sentries to moving vehicles. So it does work.

Remember to teleport the model and angle it correctly then parent it and everything else should be good to go.