Under USSSA rules, the courtesy runner must be a player not in the game.
Rule 8. Section 3B
"Players who have participated in the game in any other capacity are not entitled to serve as a courtesy runner."
So, is you only have nine players, every player much run for herself. You can not have a courtesy runner.
Some sanctions allow the last out to run - but not USSSA.
However, if a player is injured through a rule violation by the defensive team (hit by pitch, obstruction, malicious contact) then the player who had the last completed at bat (not necessarily out) can replace the injured player for on base for that inning only.
(Rule 5, Section 2.A.1)