I think the idea is they are impregnated with nenette nenetol fluid (which you can buy separate as a top up) and keeping in the container is how it stays at it's best. I've just found this article in the Telegraph
Once a popular companion of classic-car enthusiasts, the Nenette duster brush is returning to Britain. Accessory specialist Hamilton Classic has succeeded in its long-standing quest to track down the French distributor in response to a flood of requests from owners of grubby Triumph Heralds.
Hamilton boss Alastair Flack says: "I have a stand at classic car shows and club events virtually every weekend and am asked about the Nenette more often than any other product."
The brush is steeped with Nenetol, a refillable liquid that absorbs dust while simultaneously adding lustre to the curves of your Austin Cambridge.