NFL overtime rules. Say first possession offense throws an interception but then the defender fumbles trying to make a return, and the offense gets it back. The offense gets a new set of downs due to possession changing, so if they go down and kick a field goal is the game over? Or does the opposing team still get a chance.
It appears that the answer is yes, the game is over because the team that kicked off first has had their possession.
I base this on this description of a “double change of possession” source is the NFL Rules, Rule 16 (Overtime), article 5.a. note 3.
Note that “the situation” is about a foul by the defense prior to a turnover. The offense could take the penalty, and then there is no turnover and the initial possession continues. But what about a turnover during the return of a turnover, which is your question.
(Bolding added by me)
The situation in (2) may also affect the team that receives the opening kickoff during its first possession. If there is a foul by the second team followed by a double change of possession, and the first team accepts the result of the play, the second team has had its required possession, and the first team has possession of the ball for the second time. However, if it accepts the penalty, it will extend its initial possession.