The New York Giants generally do not make stupid mistakes on draft day. They do not reach for players, and they let the Clowns, Bungles, and other teams miss out on players and have them fall into their collective laps.
A guy they could go after here is Damontre Moore, but I think that he is not a Giants type of player. Sheldon Richardson is a Giants type of player, but unless the Giants want to move up to get him, he will be off the board.
The guy that probably fits best that is available is Bjoern Werner. He could be a solid outside backer if selected by a 3-4 team, but his strength is at DE for a 4-3. Werner will be a Grant Wistrom/Kyle Vanden Bosch type of player that will bookend well with Jason Pierre-Paul.
With the 19th selection the New York Giants take Bjoern Werner, DE, Florida State.