First things first, the airplane isn't going to move without someone paying for it.
Many operators publish empty legs at deep discounts. There's really no downside for an operator as the airplane typically is already paid for that segment anyway, either by the previous or the next customer. Putting the empty legs out there is an opportunity to double-dip or provide a discount for the customer paying for the segment. We'd do this going from the Northeast to Florida where we have the airplane paid for the round trip but by having a discounted leg put out to the broker community (scum) we'd often be able to fill the segment and make additional revenue for that leg. These customers generally speaking aren't the most desirable because the nature of only shopping for fire sale prices go against the grain to the convenience (and therefore cost) of private aviation. They're adapting to the situation rather than the schedule being placed around them. In our case if we were dropping the principals off in Florida from the Northeast on Thursday and they were staying for a couple weeks, we might price a little more aggressively (not at a loss) to get the airplane sold back home so they/we/the business wasn't on the hook for the 2-1/2 hour empty leg. If we could fill that leg the same or next day it was worth it to move the airplane with someone else paying for it. We liked this because the better the ratio of revenue flying to owner flying resulted in better numbers and a bigger bonus. Win!
Typically, however, it's a double dip. If the airplane costs $3,000 an hour to operate and normal retail charter rate is $5,500/hr, offering a "deep discount" on a 2 hour trip to where I was going anyway at $3500/hr then I generate $18,000 in revenue compared to $11,000 for the same $6,000 in operating costs. Profit of $12,000 instead of $5,000 for that leg. The client gets a discount and the owner gets a bonus for being in the right place at the right time and the operator gets a bigger piece of pie from which to take their percentage.
Other times the airplane is actually sold one-way because the return leg might be several hours and the customer just doesn't want to pay it. That's fine as long as the destination is close to an area where the likelihood of a live return leg is high (SoCal, Dallas Metroplex, South Florida, Caribbean Islands, NY Metro area, etc) and may be agreeable to the operator and/or the owner of the airplane. Other times if the airplane is based somewhere out of the way the first reposition leg of a trip could be discounted to make the total cost of a given trip more appealing so as to have a more competitive quote compared to another operator. Catching a double dip can help offset doing a little of this from time to time.