The fact that livers can regrow means that it's sometimes possible to take a liver lobe from a healthy donor, transplant it to someone suffering liver failure, and for both to end up with a fully functioning liver - as reported here. Recent evidence, however, suggests that this same ability means that some people's need for a transplant is only temporary, since their damaged livers may repair themselves.
Despite the focus on transplants saving lives, it shouldn't be forgotten that it's preferable if people don't need a transplant at all, saving them from major operations and a lifetime of immunosuppressant drugs. Perhaps the gap between supply and demand can be reduced, in part, by reducing demand. And, of course, it's preferable that livers that are available for transplant go to those that really need them (long term).