If a third-base coach assists a runner while a fly ball is caught legally, what happens?

In baseball, if a third-base coach assists a runner when a fly ball is caught legally, the appropriate ruling is that the runner is out immediately due to the coach's assistance. This rule is in place to maintain the integrity of the game and ensure that players rely on their own judgment and skill without outside interference once a ball is put into play. The coach's involvement in this situation is considered a violation of the rules, leading to the immediate out.

As for the other choices, they do not align with the established rules of baseball. For instance, claiming the runner is safe ignores the regulation against coaching interference, while suggesting the play should be reviewed does not apply, as the decision is straightforward according to existing rules. Lastly, the notion that the game could continue without penalties misrepresents the consequences of such actions on the field.