J/R calls this 'desertion.' See related rules comments:
6.09
The batter becomes a runner when --
(a) He hits a fair ball;
(b) The third strike called by the umpire is not caught, providing (1) first base is unoccupied, or (2) first base is occupied with two out;
Rule 6.09(b) Comment: A batter who does not realize his situation on a third strike not caught, and who is not in the process of running to first base, shall be declared out once he leaves the dirt circle surrounding home plate.
This specifically references a D3K, but applies (as I understand it) to any situation where the batter becomes a runner.
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