Penalties

Question
If the offensive side of the ball scores points to put themselves in the lead at the end of a game, but is held back by a penalty (ex. holding), does the defense have the option to end the game?  

Answer
I need a little more information to answer this question.  I believe you are asking: Can the game end when time runs out on a play where the offensive team scores and also commits a live ball foul during the last play of the period?

If this is what you are asking then the answer is yes if the foul is declined.  But if it is declined the score will count for the offensive team.

If the defensive team does not want the score to count it must accept the penalty and the down will be replayed (one untimed down)from the succeeding spot after the penalty is enforced.  The general rule is that the game can not end on an accepted foul.