I've got a cousin who'se off in mexico right now, I guess he killed a couple people and mexico will not extradite if the death penalty is a possibility.

Short of leaving the country, yes you can disappear. The easiest way is to create a new identity but even that is difficult. A homeless person can, say, go to a social security office and tell them he/she is trying to get back on their feet. They have no documentation, nothing. They say they've been on the road for a long, long time. They may not even remember who their parents are, or nearest kin. They say they are ready to start getting back on their feet and back into society. They say their name is jane doe, the office has no evidence to the contrary, the office HAS to issue a card and a new social security number to jane doe. Jane doe takes this to the DMV and gets a state I.D. card. Jane doe takes these two and opens a bank account. Jane doe takes all those and buys a car and a house, starts a credit reccord, and a completely new life.

but Jane doe MUST become jane doe, regardless of who she was beforehand. she must cut off all ties to the past.

Identity is a funny thing. We think of it as a concrete, but it is actually abstract. It is a perception, a self perception rather than an absolute. you can BECOME jane doe, and if you do, if you really are that person, you are not committing fraud. But if it is just an alias, a secondary identity, you are committing some serious fraud with federal accountability. If Jane Doe was ever found to have a different identity in the past, jane doe can expect serious legal repercussions, but truly owning up to the new identity, depending on circumstances and motive, will often allow for fairly solid legal grounds for defense. It is still of the utmost importance that Jane Doe never compromises her new identity at all. Not even to her new spouse years down the road, or dearest friend confidante.

You can look up all kinds of helpful articles on 'how to disappear' but I would reccommend doing it from a public computer, well in advance of your actions and do not discuss it with anyone.