Yes indeed, though I've never suffered the ultimate cruel fate of broken string.
There's rarely much advice on how to wind the string round the peg. That can make a big difference and save a lot of bother, especially for big fat A and E. Also depends where the hole sits on the peg.
What order to replace? ... how far to pull the string through the hole? ... whether to trim the excess (pretty much never - except gut!)? ... whether to wind all in one direction (if there's room for the coil between hole and edge of box), once round behind the excess then switch direction (ideal, if there's room?), or risk coiling one way then crossing over the coil to continue in other direction (not advised, looks shitty, but widely done)?