Sometimes.

Why are you asking?

Makes sense that they would, it would be a lot cheaper if everybody believed the (witness protection) person was dead, rather than the cost of keeping them alive, but secret.

HowStuffWorks "How Witness Protection Works"

Normally no, most people in the witness protection program are just other criminals who turn evidence against others they are working with or for.

They even have to serve prison time ( under other names) in specific federal prisons.

So no most just go away.

Also they can't be "dead" they have to be physcially in court and testify, they will sit on the witness seat in front of the person they are testifying against. So they know they are alive and know they are testify against them.

The "deaths" are good for TV since the witness with a new ID in real life just serves a few years in prison before going to a new life.