While reading this question, I recalled that I had read a similar story in my English textbook. The details were a bit different from this question though.
An alien (who I think is a convict) convinces a human to exchange consciousnesses with it because it wants to be free. The human appears to be reluctant but at the end, it is revealed that
the human is suffering from some disease and will die soon and is happy to have gone through with the exchange.
I read it ~10 years ago at school and some of the details are probably wrong.