I saw this in another thread here, posted by Mike Boozer, so it's official (he emphasized the bolded text). So at least you know badges/tickets can be replaced if they are lost or stolen, despite the sell-out. Unfortunately, you'd have to pay full price for them...
Here is the policy:
Lost & Misplaced Badges & Event Tickets
We cannot replace lost, stolen or forgotten badges and/or event tickets. Please be responsible with your convention materials. Lost, stolen or forgotten items must be repurchased at full cost. It is recommended you check with the Gen Con Show Office to see if your materials have been turned in to Lost & Found before buying new materials. Gen Con LLC assumes no responsibility for lost, stolen or forgotten materials.Gen Con LLC is not responsible for items lost in the mail (via the U.S. Postal Service) or items marked “delivered” by the USPS tracking system. If you chose to have your items shipped via USPS, we will reprint your badge and event tickets, as long as the USPS site lists your package as “lost” or not yet delivered. If you chose USPS and the package is listed as “delivered”, you will be responsible for purchasing a new badge and any associated tickets. Any returned mail will be available for pick-up at the Will Call kiosk onsite.
To be clear you can repurchase items that are lost, stolen, or forgotten. They are still in the system. We will replace USPS items if they are marked "lost" by the USPS, or if they were not delivered. If they are returned to us you can pick them up at the Will Call kiosk onsite.
Customer Service & Event Team Manager
Gen Con LLC