Yes, I knew you'd be thinking of a rubber balloon but I was thinking more of a "football". I was thinking of a fiber bag with a rubber bladder. Deflating the bladder allows you to collapse the "balloon" (the bag) and feed it and position it in the tube. The fiber bag would restrict the size of the "balloon" (the bag) as you inflate it, preventing the unsupported ends from simply stretching.

This is what they do as angioplasty.