Spot and down
 

2nd and 8 on the 50. A runs for no gain. After the run is over, B1 slugs A1 and A1 slugs him back. Both are flagged.
After assessing both penalties, where is the ball spotted and what is the down?

Dead-ball flagrant personal fouls for A1 and B1. Penalties offset, but A1 and B1 are both ejected.

3rd and 8 from the 50.

In NFHS these fouls would not offset. The penalties are enforced in the order of occurrence. The penalty for Team B's foul would be enforced first, giving Team A a first down since they reached the line to gain with Team B's penalty. Next the penalty for Team A's foul would be enforced, backing up Team A back to the 50. The chains would be reset and it'd be 1st and 10 for A at the 50.

In NCAA these fouls would offset and the down counts. 3rd and 8 for A at the 50.

In either case, both players are disqualified.

Dead ball fouls are enforce in the order they occurred unless the order cannot be determined. In this case the order seems fairly clear. First and 10 from the 50. While the yardages do offset in this case, the penalties do not.

B's first foul makes the line to gain for A resulting in a first down, A's foul moves the ball back to the 50 where it will be first and 10 for A.

See 10-2-5 and 10.2.5 Sit A