Microsoft Research's approach gets around this by re-encoding all the pieces, so that each one that is shared is actually a linear combination of all the pieces, fed into a particular function. The blocks are then distributed with a tag that describes the parameters it contains.The system looks intriguing, especially if it can lower overall network traffic by allowing users to assemble an entire file without all the component parts. You can read more on the approach in this research paper (PDF) on the subject.
Once you have downloaded a few of these, you can generate new combinations from the ones you have, and send those out to your peers. Collect enough of these pieces, and you will have enough information to reconstruct the whole file. Even if you don't have all the original pieces distributed by the person who held the original version of the file.