Instead of flexible wire that gets all tangled up, use rigid wire
sections that plug into each other and fold at the edge or in the
middle.
The result: a long wire that you can fold up or break into
pieces, with less flexibility than a regular wire but still is
somewhat flexible (depending
of course on the length of the
sections.)
Each section tip has a connector to plug into the next section.
There will be different types of plugs that connect into the end
section, for input and output: e.g. for USB, for electrical
current, for an audio signal. The plugs for input can be RJ, USB
etc, and for output you could have an earphone, a USB out, a
charger plug etc.
2 ways to do this.
1. Each section's tips with the connector are extended by a
wire. Allowing the plug to turn in any direction.
2. Or, somewhere in the middle, there is a joint or wire that
lets it fold. Best if it the joint has two positions: a) free to
move and b) rigid - flat.