My experience is that if you can smoothly unravel a ball of yarn from the outside, you can also smoothly unravel it from the inside---if you can get hold of the end buried in the ball and cope with the ball going floppy once the core has been removed.
Is this mathematically or thought-experimentally provable?
UPDATE (MORE DETAIL): I am interested in the behavior of real world balls of yarn (e.g. sheep wool). Specifically, I want to know whether a certain way of wrapping a ball of yarn might introduce some kind of knot or tangle that prevents it from being unwound from the inside-out, yet still allows it to be unwound from the outside-in.
It depends a bit on what you are allowed to do. If I am allowed a very long, thin, flexible pair of tweezers that can be directed inside the ball then I start at the external end, trace along the thread to the other end, and then pull it back along itself.
However, if the tweezers are straight then it is rather less obvious. If the tweezers are only as long as the radius rather than the diameter it is harder again, as unless the inner end is in the centre, the choice of entry points is limited.
Friction is also relevant. If the thread is slippery enough then the whole thread may just slide along and you will see the out end move as you start to pull the inner end.