I wonder why people are so eager to combine different hash algorithms, especially a strong with a weaker one. If this is isn't a well-established anti-pattern, it should become one.[1] Why? Because in some sense it combines the weaknesses of both algorithms.

Assume your password hash is:

h(p) = bcrypt(sha512(p))

Assume in the future somebody generates a sha512() collision with p and q, while bcrypt() holds water:

sha512(p) = sha512(q)

It follows that:

bcrypt(sha512(p)) = bcrypt(sha512(q))

and hence:

h(p) = h(q)

So any collision in sha512() translates directly to h(), bcrypt's strength is unable to protect you from that.

Had you just used bcrypt(), you would not have been affected.

Frankly, this is about collision and not about preimage attacks (the latter being more relevant for password cracking), but the former is usually a first step towards the latter. Also, this example demonstrates that combining a weaker and a stronger hash algorithms usually does not combine their strengths, but their weaknesses.

[1] It is almost like inventing your own crypto primitives, which actually is a well-established anti-pattern.