According to the rules, when can umpires call time to exchange wet softballs?

Umpires can call time to exchange wet softballs only when all runners have stopped. This allows for the game to maintain its flow and ensures that a pause for ball exchange occurs at an appropriate moment. If the runners are still in motion or attempting to advance bases, it can create confusion and disrupt the game, so the rule emphasizes the importance of having a clear cessation of play. Timing the exchange of balls during such moments helps maintain the focus on the game while ensuring that the players are adequately prepared to continue with dry equipment.

The other options do not align with the regulations that govern game play. For instance, exchanging wet softballs before the pitcher secures possession could lead to potential delays right when a pitch is about to be made. Similarly, waiting for the end of the game or only at the end of an inning would not allow for timely exchanges when necessary during the game. Accepting wet softballs can disrupt the playing dynamics significantly, which is why the emphasis on timing is crucial.