BitcoinTalk
Major Meltdown

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Here's an answer to a similar question about how to recover from a major meltdown.
https://www.bitcoin.org/smf/index.php?topic=191.msg1585#msg1585

If SHA-256 became completely broken, I think we could come to some agreement about what the honest block chain was before the trouble started, lock that in and continue from there with a new hash function.

If the hash breakdown came gradually, we could transition to a new hash in an orderly way.  The software would be programmed to start using a new hash after a certain block number.  Everyone would have to upgrade by that time.  The software could save the new hash of all the old blocks to make sure a different block with the same old hash can't be used.
However, if something happened and the signatures were compromised (perhaps integer factorization is solved, quantum computers?), then even agreeing upon the last valid block would be worthless.
True, if it happened suddenly.  If it happens gradually, we can still transition to something stronger.  When you run the upgraded software for the first time, it would re-sign all your money with the new stronger signature algorithm.  (by creating a transaction sending the money to yourself with the stronger sig)