Christine,
You are correct the hand is not dead but I generally like to give a warning before I give a penalty. I presume player 2 does not put chips in to call and is last to act, in that case the hand plays but a warning should be given at the end of the hand and then a penalty at the end of future hands. If Player 2's cards were over the line I would rule it dead. The fact that the river has been dealt does not matter, the cards would still be in play if it was done preflop, flop, turn and river. If the player exposes his/her hand with action pending the player has all options open to them check, bet, raise, call and fold but has the disadvantage of players knowing what he/she has.
Hope this helps!
Andy