Do you want something different written to the string indicator in the False case, even if it is an empty string?
Or do you want the string indicator to keep the same information as when the case structure was true?
If the first, then you will need to wire something into that tunnel in the false case. (If an empty string, then you can wire that, or right click on the tunnel and select Use default values if unwired.)
If the second, then move the indicator inside the true case.
