Close the door often means to totally exclude from an opportunity or to make it impossible for something to happen. I don't know what sb is referring to, but if you could provide some context I might be able to figure it out.
Oh I see. It likely is referring to completely ending any type relationship with that person. In other words, to leave them in the past and not look back. It has a kind of finality, like they are cutting off all contact or at least putting some closure on the relationship. It doesn't have to mean a romantic relationship either.
The other thing it could mean is they are preventing that person from some opportunity.