In the given hypothetical, there was no live-ball foul. Get off the field and go home.
Of course. If there is a live-ball foul, that penalty is completed, and, if necessary, then the penalty for any dead-ball foul is completed. If, by rule, another down is to be played, then, yes, the period is extended.
So, you ask, "How can you know there has been a live-ball foul" (which would compel you to call the dead-ball foul)? Take that quick look around, and see if there was a foul called. If so, then throw your flag for the dead-ball action. If it was a foul then, it is still a foul, now. But, if no live-ball foul, see above.
PS If there was a live-ball foul, make the calling official show you the police report.
