When you dream of the birdcage, then such dream indicates the desire for freedom. Perhaps you are or you feel that you are locked up in the place where you are unable to express yourself. There is a possibility that someone in your life is trying to take the control over you.
Dream dictionary: Birdcage dream meanings
…If the birdcage or aviary has any bird in it that means a good omen, in general regarding love or friendships. If it’s empty it’s an omen of sorrows about love or lack of love….