what do I do if the owners do not pick up their dog the day they are supposed to?

As Walt said, you need to contact Rover Customer Support.

Here's another example of what happens when you discount your services. I realize you have low rates because you are new and trying to establish a customer base. However, people who haggle are showing they don't consider you a professional. They seem to be the source of many problems posted here. So it doesn't surprise me that they don't want to pay for another night.

Dropoff and pickup times need to be established at the beginning to ensure proper pricing. Also, you should always get a local emergency contact. This way, if they don't pay, then you would tell the people that their emergency contact needs to pick up their dog by X time.

Good luck.

First I would call Rover support @ [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team] while it is unlikely they can do much to help your physical situation they will help you with the client in trying to collect the additional fee. I would try to keep all the dogs physically separated to cut down on the possibility of a skirmish. Best of luck and I hope the support team can help you

In my opinion, this would be considered neglectful ownership and abandonment. If it were a child left after hours in a daycare and no one could be reached staff would have to call the proper authorities. I would definitely call Rover to get some guidance around this but as it is negatively affecting your subsequent bookings I might suggest calling your local animal control and having them picked up. Let the owners pay for getting them out of the pound if they won't pay you for the extra time and inconvenience on your business. At least they will be safe and cared for and these owners will be required to answer for their behavior.