Untimed down
 

A comes to the line with :36 seconds left in Qtr., they false start at :20 seconds, the penalty is accepted. A doesn't want to run another play.

Does A have to run a play??

Can a period end on an accepted penalty??

No, don't have to run another play in your example.

Foul did not occur during the last timed down.

(However, if the white hat felt that A intentionally false started in order to illegally consume time, he will start the clock on the snap, not the ready.)

R U asking for an NFHS ruling or an NCAA ruling?

NFHS--But can you end a period on an accepted penalty???

Yes, if it didn't happen during the last timed or untimed down. A false start does not happen during a down. The accepted penalty is only part of the equation. See 3-3-3, bottom of page 39.

It's misleading to describe that as "on an accepted penalty" rather than after one. An interval intervened after its enforcement.