My understanding is that - unless something happened recently - he is still alive. He left the Muppet Shop sometime in the late 80s/early 90s. A puppeteer I know toured the shop just after he had left and kept asking them about Faz but everyone was very uncomfortable answering questions and wanted to change the subject very quickly. This person had the impression that Faz left under difficult circumstances but he wasn't sure as no one was willing to clarify that, which is understandable. That's a rumour, not esthablished fact.
If you read between the lines in a lot of the sources of information on the company you kind of pick up on the fact that everything wasn't always "smiles and sunshine" at Henson and some of the employees did not always see eye-to-eye with the company. I think things were increasingly strained in the 1980s when the company was busy and Jim Henson wasn't able to do much day-to-day supervision (one of the reasons the original sale to Disney was arranged).
That's not to say it wasn't a great place to be and work, just that I've never entirely bought in to the myth that the entire company was always 100% cohesive and conflict-free. Ups and downs and the odd falling out between people are the norm in creative organizations. Even Frank Oz has been quoted as saying "Jim Henson should have f--kin' fired me several times."