When R1 attempts to steal second base, what should happen if F1 does not throw to second fearing R3 will advance?

When R1 attempts to steal second base but F1 does not make a throw to second base due to the concern that R3 will advance, the proper call is that R1 is allowed to remain on second. This situation arises because R1's attempt to steal is a legitimate action, and if there is no throw made by the catcher (F1), then R1 has legally stolen the base.

In this context, R1 is not forced to return to first base, and no violation occurs just because the pitcher chose not to make a throw to second. Additionally, the concept of a force out does not apply here since R1 was stealing and was not obliged to return to first base. The rule regarding leaving the base early typically applies to the scenario of a runner leaving a base on a pitcher's delivery or a fly ball situation, which is not relevant in this case since there was no throw and thus no infraction by R1.