Hope this helps. There are two sections in the USSSA Rule book that talk about your situation.
under Rule 8 Base Running. In your case, Sect 18 is more appropriate since the player had reached first, hence they become a runner at that point and no longer a batter-runner
Sec 17 The batter-runner is out;
J. When, after becoming a batter-runner, they do not attempt to reach first
base before all infielders leave the diamond, the half-inning ends, or they
give up by entering the bench or dugout area.
EFFECT: Ball remains Live
Sec 18.Any runner is out when the runner:.....
X. a runner on base leaves the game without a replacement substitute
Here is a website that has an electronic copy. I am sure it is somewhere on the USSSA site too. https://www.cornerjackets.com/Uploads/2015FPRuleBook.pdf