Theory:

     “Wake up, wake up, little bird,” she said.

     She began to cry and her tears fell on the little bird. He opened his eyes and saw that the bars of the cage were no longer around him.

     “I cannot sing unless I’m free, and if I cannot sing I die,” he said.

     The Princess gave a great sob.

     "Then take your freedom,” she said. “I shut you in a golden cage because I loved you and wanted to have you all to myself. But I never knew it would kill you. I love you enough to let you be happy in your own way.”
Explanation:
 
Concerned about the bird's welfare, the Princess requested that it awaken. Her tears fell on the small bird as she had an emotional meltdown.
 
The bird said that he couldn't sing a song unless he were free to travel around.
 
September wept nonstop. She eventually consented to let the bird go. She also mentioned that she had locked the bird in the gilded cage because she adored him. She claimed she desired to have him all to herself but had no idea that doing so might kill him. She said that she loved him sufficiently to allow him to be happy in his way.
 
The theme of the narrative is expressed in the statement, "I cannot sing unless I’m free, and if I cannot sing I die." In this narrative, when the bird was in his preferred setting, he composed several calming tunes. However, when confined in a cage, he refused to eat or sing. His unwillingness to return to his regular personality became a significant source of anxiety for the Princess. As a result, the Princess had to choose the bird's freedom above her love for the bird.
 
The bird's confinement had influenced his creative attitude. Similarly, a person with artistic abilities (such as dancing, singing, sketching, etc.) will work effectively in a favoured atmosphere. In other words, the ideal atmosphere promotes higher levels of creativity. The creative brains refuse to operate when pushed to be inventive (like how September forced the bird to sing).
 
'Caging of someone' is a common metaphor. This phrase can be interpreted in many ways. However, most commonly, 'Caging of someone' is referred to people with power defining the social stature of the weak by cutting out the possible prospects of growth.
Reference:
National Council of Educational Research and Training (2008). It so happened. Princess September - Somerset Maugham (pp. 34 - 44). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.