empailler

To stuff a dead animal for display (taxidermy: empailler un animal) or to put straw padding into something like a chair seat or a bottle for protection — the common thread is packing something with straw or straw-like stuffing.

• Le taxidermiste a empaillé le renard pour le musée. — The taxidermist stuffed the fox for the museum.
• Autrefois, on empaillait les chaises avec de la paille tressée. — In the past, chairs were seated with braided straw.
• Les bouteilles étaient empaillées pour éviter qu'elles se cassent. — The bottles were packed in straw to keep them from breaking.

The taxidermy sense (stuffing an animal) is by far the most common use today — the straw-chair sense is more of a traditional-craft context.