^Echothree excellent question and by having the various format starter packs I have duplicates of Mr Incredible, Jack Sparrow and Sulley so can answer that from experience.
If you buy a replacement from a store, it will be blank (unused, unless it was used to demo) and like the first time you use a figure it auto takes ownership (hence all the people being confused about taking ownership since the game does it automatically on unused figures), same will happen except instead of starting at level 0, it will load the figure with the experience level you achieved before.
If you buy a secondhand replacement from eBay, it will come up as a Guest, once you take ownership from the pause menu it will be yours and restore your experience level from your game data.