The nose cone shells are called payload fairings. Once outside the atmosphere the fairing is jettisoned which exposes the payload to space.
The SpaceX fairing separates into two halves. Fairings usually burned up in the atmosphere or were destroyed upon impacting the ocean. On March 30, 2017, SpaceX successfully retrieved a fairing intact for the first time in history. This was after the fairing was parachuted into the water. They want to parachute it and then catch it with the boat and the giant net.