One of the most moving songs I have heard is "A Change Is Gonna Come" by Otis Redding. This is a rather sad ballad, performed, however, with great feeling and a sense of hope. Though I am not sure how you would render the song into something danceable, I am sure you could come up with a method.
If you want a classical piece, why not choose an aria from one of the tragic operas? For instance, in Act IV, Scene 2 of Giuseppe Verdi's Aida, Radames has been thrust into the crypt in the Temple of Vulcan and awaits death. As he does so, he utters a quiet wish that Aida may be happy wherever she is, and never learn of his dreadful end. Soon, however, the figure of Aida is seen approaching and has been waiting for Radames for three days. Radames attempts to lift the stone and free her are futile.
Aida sings her last farewell to earth (O terra, addio), and Radames joins in with her. A poignant duet, indeed.
Interesting! Do you want a piece of music with words? There are some really haunting songs in Les Miserables, and I think they would be beautiful to dance to. I also like piano sonatas. Then again, you could go completely in the other direction and use a blues song.
No doubt your question will get many varied responses. Some of the old Southern gospel hymns can portray pain, suffering, and redemption. These hymns have been sung for hundreds of years and many were written by slaves in the old south.
suggested pieces both with lyrics and without are greatly appreciated