I'm thinking in particular of SHA-256, what would happen if tomorrow this algorithm became completely obsolete?
Any algorithm doesn't suddenly become completely obsolete though. And cryptography become obsolete usually doesn't mean it can be cracked without big resource. Even google spend tons of resource to perform SHA-1 collision.
Shouldn't there be an alternative solution before that happens? I'm not necessarily talking about including this "new replacement code" in the Bitcoin code, but at least having the code on hand, ready to replace the current code.
There are many tool and library (such as OpenSSL) which already include newer cryptography algorithm. Bitcoin developer could use it, although the harder part is soft/hard fork and ensuring there's no implementation bug.