The Mexico native being held on drug-related charges was clothed in a blue county jumpsuit, and rubber boots that inmates working the cafeteria wear, KTSM said.
Medina-Bailon's body appeared to be crushed, U.S. Marshal Robert Almonte told the El Paso Times newspaper.
Sheriff Richard Wiles earlier told KTSM that Medina-Bailon was working in the kitchen and may have sneaked by two jailers on duty and dodged monitored security cameras to hide in the bin.
"We believe he managed to hide in the trash and was able to get into an area which at some point became unsecured when the gates were opened to allow vehicles in and out of the facilities, and that's how he escaped," Wiles said.
KTSM said Wiles was surprised that other inmates hadn't escaped through the trash before. Two years ago the county went from small garbage cans that are hauled out to large dumpsters that are picked up, but security stayed the same, creating the window of opportunity for inmates to escape.
The sheriff's office told KTSM that Medina-Bailon didn't have a criminal history showing he was violent, but he had connections to some dangerous people.
"Clearly there's a connection to drug cartels, he's a distributor, a smuggler, so to what extent we don't know," Wiles told KTSM.