Or what would happen if improved cryptography comes along, how would the protocol deal with this? Would a layer on top of the current protocol be enough to patch it up or will Bitcoin die?
Bitcoin is an open protocol, everything can be changed, patched , and so on.
Ultimatively, if sha256 gets to the point where its useless, bitcoin would have to switch algo, making all asics useless.
Would be a fun thing to see, also becose the price would have a major dip, where u could buy, knowing there will be just as powerfull rebound.