How is a fork of bitcoin achieved?

[ulhaq]

There was the bitcoin cash fork and now the bitcoin gold fork, but the question is, technically how is this possible? The private keys from bitcoin are valid on the new fork, yet whoever creates the new fork does not have access to these passwords.

It would be as if I created a new website and used people's facebook usernames and passwords, which were valid on my site, but with me not knowing anyone's passwords.