The period is not extended. We need to remember that "loss of down" is the abridged version of "loss of right to repeat the down" and although there isn't a down to repeat after a change of possession , the loss of down provision on the penalty would remove it for qualifying for an untimed down. The following play occurred in Louisiana several years ago that prompted this :
(1) K has just taken a 2 point lead with 10 seconds to go;
(2) K kicks off to R;
(3) R's return turns into a rugby scrum;
(4) At K's 15, R1 is about to be tackled and heaves ball toward K's end zone;
(5) R2 catches the airborne heave in end zone;
(7) more flags
than a parade;
(8) K needs to accept IFP to cancel score = ball @ K's 20 & untimed down;
(9) enter Hans, a former soccer star, his 37 yard FG is true, Hans is the hero and heads off to the bayou with the prom queen;
(10) the following January ,Louisiana proposes this rule change;
.....and now you know the rest of the story
BONUS QUESTION : Which has more counties, Maine or Louisiana??
NOTE : While said story is true, Hans and the prom queen were only fictional .