Sha256 will be replaced, but even if it's cracked before a replacement, there are alternatives ready to be deployed with a fork. It'd be ugly but not lethal.

Changing the hashing functions, encryption, and network verification are all built into bitcoin. It's designed to be resilient, and to use consensus when adapting over time.

It'd be really stupid for people to go "oh no, someone cracked sha256 and mined a million blocks, I guess we're done with bitcoin now. Buh-bye money!"

They'll fix it in the case of a noticeable exploit. If someone were clever, they'd mine blocks surreptitiously, sufficiently spaced out over time and different networks so that it looks like normal mining. They could get a few blocks per day for maybe a couple years until the upgrades. The impact to the system would be minimal.

If and when sha256 is broken, the internet breaks, period. It will be a Y2K-like event across the world. Every single banking website would be vulnerable.

The Bitcoin core devs have been thinking about the failure modes of hash algorithms since Satoshi. If you are betting against Bitcoin primarily because you believe it will fail when sha256 inevitably falls, you are missing the bigger picture and underestimating the resilience of the Bitcoin developers and broader community.

The security of Bitcoin doesn't depend on SHA256 the way you think it does.

I wonder: if somebody would silently break sha256 and was able to mine an almost arbitrary amount of Bitcoin would it be unethical to do so? (Or illegal, which would probably depend on the jurisdiction)

I feel like it would be slightly unethical but on the other hand you're not really defrauding anybody. You did actually produce those blocks, not by improving your calculator but by using some other method.

Got details on how sha256 is broken?

Can't wait!