A new steering stabilizer will not fix Jeep death wobble. It's a shock absorber for your steering linkage that reduces the shaking feel, but doesn't address the worn track bar, ball joints, or tie rod ends that are actually causing it. Replacing only the stabilizer masks the problem temporarily, and it returns.
This is one of the most common misunderstandings around death wobble. A new stabilizer can make the Jeep feel noticeably better for a short time, which leads many owners to think it worked. But the play in the front-end components that allowed the wobble to start is still there. The stabilizer is fighting that play on every drive, and as soon as it wears down slightly — or the underlying parts wear further — the wobble returns, usually at lower speeds and with less provocation than before.
A stabilizer does belong in a complete death wobble repair, but as the last step after the worn components are replaced, not as the whole repair. If a shop quotes you only a steering stabilizer for death wobble, ask what's being done about the track bar, tie rod ends, and ball joints. In Ann Arbor, Hoover Street Auto Repair will diagnose the actual root cause and replace what's genuinely worn — the stabilizer is part of that job, not a substitute for it.