An empty leg is a one-way repositioning flight: the aircraft — a Gulfstream GV — has to fly Greenville to Saint Paul anyway, so the whole cabin is offered as a single one-way charter at the operator's repositioning rate rather than a round-trip one. You charter the aircraft, not a seat, and the date and route are fixed by the operator's own schedule. This leg covers 1,044 miles, about 2h 12m in the air. The cabin seats 14.
Empty-leg inventory turns over continuously — a leg is live until the operator sells or cancels it. If this one is gone by the time you call, the links below show what is live on the same route and at the same airports right now.