The song was a farewell. It was a transfer of ownership. She was telling him that even though he was walking away, he was taking her soul with him.
Surrender: It highlights the peace found in finally admitting one's feelings and "giving away" the burden of a lonely heart. En Idhayam Thanthu Vitten Anbe Song
The director uses the "walk and sing" trope effectively. The hero never dances; he stumbles. This realism is why the song feels less like a performance and more like a confession. The song was a farewell