R1 is on first base. No outs, and team B's nineth batter is at the plate with a 1 ball and 2 strike count on her. The pitcher of Team A throws an illegal pitch that is down the middle of the plate for strike three. The runner at first is going on the pitch. The ball gets away from the catcher. R1 goes on to third base. The batter forgets to run to first and is tagged out by the catcher. I know the penalty for an illegal pitch is the pitch is ruled a ball and base runners are awarded one base if the ball is not hit or batter becomes base runner. Otherwise,if ball is hit,Team at bat has choice of accepting play or penalty. Does R1 have to go back to second and the count is 2 balls and 2 strikes on B9, or can the coach take the play and let R1 stay on third with 1 out and have B1 coming up to the plate with one out.

Since the batter becomes a runner immediately on strike 3, I'd say that the coach has the option to accept the play, 1 out, runner on 3rd, leadoff batter at the plate; or the penalty, 2-2 count on the batter, runner on 2nd, no outs.

This is a long way of saying the IMO, Yes, the coach can take the play if he chooses.

Willie,
You didn't say who's rules we're using here, so here's what 3 organizations say.

For ASA and NCAA, an illegal pitch is a delayed dead ball. Since the batter did not hit the ball (BR must safely reach 1B & all other runners must safely advance at least 1 base), the offense's coach is given the option of taking the play or having the illegal pitch penalty enforced. See EFFECT for illegal pitches, it's listed in Rule 6 right after Section 8.

For Fed rules, the difference is that the manager/coach is always given the option of taking the play or the penalty.