Firstly, this is really only appropriate on devices that are retractable, as non-retractable devices can (and usually do) have stiff cords already. The only device where this feature matters that I can think of is on a mouse.
One feature of various devices that is both a blessing and a curse is that the first inch or so of cord on a device does not generally curve enough to perfectly wrap around the device. On a mouse, this feature is usually a blessing, as it makes the cord less apt to hit the hand of the user of the mouse.
On a mouse with a retractable cord, this feature is not present, because the cords are thinner and more flexible so as to make them store better when they retract. There's often about a centimeter of thick somewhat curve-resistant cord at the tip of even retractable mice, but this is not enough. The most common type of retractable mouse cord is a spinner cord, rather than having the cord retract into the mouse.
I propose that about an inch of the cord, which will be thick, retracts into the mouse itself as a separate feature from the retracting spin box found outside of the mouse. Users who disliked this stiffness need never make use of it, since it retracts. But those who find the cord on their retractable mice is wrapping around their fingers may appreciate having the first inch of the cord be inflexible so that the cord will stick out from the mouse. This device probably wouldn't be so easy to incorporate on the smallest lines of the portable mice.-- aguydude, Jan 28 2008 I think you're talking about a strain relief and it's there to protect the part of the cord most likely to be damaged by constant flexing and pulling. Having it retract would defeat its purpose.-- phoenix, Jan 28 2008 The cm needed for strain relief doesn't need to retract (and shouldn't, as then the cord would be rubbing against the edge of the hole). Anyhow, I'm giving it a secondary purpose.-- aguydude, Jan 28 2008 I assume that it would retract for storage [+]-- marklar, Jan 28 2008 Consider a collar filled with magnetorhelogical fluid around the strain relief portion of the cable. When the Universal Serial Bus is connected, it supplies voltage needed to change the viscosity of this fluid, and it becomes more rigid. When the device is unplugged, it becomes more pliable. I am unsure if the diameter of this collar could be nontrivial.-- ed, Jan 28 2008 random, halfbakery