When in a situation where the ball eludes the catcher on a half swing which the plate umpire rules ‘no swing’ (and therefore a ball) and the batter would be entitled to run to 1B if the call resulted in strike 3, the plate umpire should appeal to the appropriate base umpire immediately without waiting for a request from the defense. This will give the batter the oppourtunity to run to 1B without delay should the call be overturned.
Below we have a video depicting an example of this scenario. With 2 outs, R1 and R2, and a 2-2 count, the batter checks his swing on a ball in the dirt. As you see, the plate umpire immediately and voluntarily requests help from U1, who ultimately rules ‘no swing’