There isn't any specific single VI in LabVIEW that implement the same functionality you described. However, it is possible to program the enable behaviour with a few extra VIs.
The following screen capture shows how the enable functionality was implemented using LabVIEW's logical functions and memory blocks present on the LabVIEW Control Design and Simulation Module. The VI on the top left implements the main functionality and the extra logic (in the red circle) add the extra feature you are looking for.
Hope this helps
National Instruments Control Design and Simulation
You can also download the Control Design and Simulation module and evaluate it for free during 30 days. The link for the download is