Shevuos 4:9

If a person calls upon witnesses to testify for him when they become aware of evidence that would help him, they are exempt. This is because their oath preceded them having the information they would later withhold.

Shevuos 4:10

Let’s say that a litigant stands in the shul and says, “I call upon you that, if you have information on my behalf, you come and testify for me.” In such a case, the witnesses are exempt until the litigant addresses them directly.