The moth eats the fur, and some furs are not allowed across the street without papers, let alone across the border. In the overview Security for collectors fur sits with textiles and at the legal line, next to Ivory and CITES.
The limit
Which species you may own, buy, and pass on is not on the label in the collar. It is in species-protection law and on the papers that come with the piece. You ask before you buy. This text is not a buying guide.
What gets ruined without a thief
Moth, heat, a plastic cover with no air, light. You store cool, dark, and breathing, and you check. An infestation moves into the whole cabinet. You separate at once.
When someone comes
Bulky, but a small jacket goes along. It does not hang on the door. The papers lie in the document cabinet, the piece in the cool cabinet, not in the hot safe.