What is the bird and/or the birdcage supposed to represent while Hank and Leticia have sex?

In Monster's Ball, Hank and Leticia have sex in her living room. They engage in extremely passionate and unbridled sex during this scene.

During the scene, we see close-up flashes of a brown-skinned female hand reaching into the cage in an attempt to capture the bird. The bird cannot be caught and flaps its wings. As the sex scene progresses, there are more quick flashes of a female hand attempting to capture this bird. At the end of the scene, the bird is caught and held in the female hand.

We never see Leticia actually putting her hand in the cage or holding a bird...we just see a hand. Also, there is a birdcage in the background on a dresser while Hank and Leticia have sex.

What exactly is the bird and/or the birdcage supposed to represent? It doesn't seem possible that her hand could go into the birdcage in real time given the physicality of their lovemaking. Was this actually Leticia's hand?

NOTE: I did not include a clip of the scene referenced due to the graphic nature of the scene. Unfortunately, I have searched for still pictures of the hand in the cage and have not found any available.