It's Technically Not Illegal To Fake Your Own Death, But...

...you would invariably break other laws, especially involving taxes. Or if somebody made a life insurance claim. Or any police or government report involving the supposed death was filed. Being able to start fresh, under a new identity is a fantasy for a lot of people, but extremely difficult to pull off. Of course it wouldn't help if you were a famous musician who then decides to play out, even in the smallest out-of-the-way dive bar.