They don’t get the additional yards. They could run all the way to the end zone and the play would still be dead.

It’s the same as if a defensive player picked up the (dead) ball on the ground and ran it to the end zone. They don’t get the ball or a touchdown. It’s the same for both offense and defense.

On the other hand, if the play is blown dead and an offensive player goes and hits a defensive player, it is a penalty, just like it would be against the defense. That happens pretty frequently.

Several people have said “there should be a penalty for an offensive player too.” There is, and it’s the same penalty. And running after the play is over is not the same thing as tackling a player.