Why does 0x00 make bcrypt weaker? On the following site:

https://paragonie.com/blog/2015/04/secure-authentication-php-with-long-term-persistence

when talking about the dangers of using bcrypt it states: 


  There is a nontrivial chance that one of the raw bytes in the hash
  will be 0x00. The sooner this byte appears in the string, the cost of
  finding a collision becomes exponentially cheaper.


I am not fully understanding what this means and how 0x00 would result in finding a collision sooner than any other hex digit. Can someone explain this more clearly to me. I also do not understand why sending it through base64_encode would make a difference as the password will still be the same and can be decoded with base64_decode.

Also, on this page it states that using base64_encode will get around the 72 character limit of bcrypt. However, if the bcrypt algorithm limits any input to 72 characters why wouldn't it also limit the base64_encoded string to 72 characters?
In many cases, 0x00 is treated as end of string. That is where the problem comes into play. So if I passed password\x00defgreallylongpassword into bcrypt, the password would be terminated after password due to the null byte. That is a very insecure password and can easily be found with a dictionary attack.

No one types null bytes into a password field, however. Where the blog post says this can occur in practice is if you first hash the password, then run it through bcrypt. There is a chance that the hash digest will have a null byte in it, which will cause the bcrypt code to truncate it.

The poster gets around this by suggesting that you base64 encode the hash of the password before feeding that to bcrypt. The base64 encoding will not have null bytes.

This hash then bcrypt construction has been proposed as a way around the 72 character limit of bcrypt. That said, I agree with this answer on our sister site. If you are using bcrypt for values that you expect might be larger than 72 characters, you are probably not using bcrypt for its intended purposes and should rethink what you are doing.