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A baryon is a subatomic particle, a hadron (a group of elementary particles that experience strong nuclear force) with a non-integer spin. Baryons accumulated aboard starships as a result of warp travel. They could be removed at facilities that performed baryon sweeps, a procedure lethal to organic material.

Captain Jean-Luc Picard was trapped aboard the USS Enterprise-D during a baryon sweep at the Remmler Array in 2369. (TNG: "Starship Mine")

When Quinn transported the USS Voyager from 2372 to just before the Big Bang, a build-up of baryonic particles was detected outside. (VOY: "Death Wish")

Baryons are heavy subatomic particles, including protons and neutrons. As almost all normal matter in the universe contain these particles, a process which eliminates baryons wouldn't leave much behind. We can assume that the baryon sweep refers to a specific type of heavy subatomic particle created by the subspace field of warp drive, rather than the entire family of them. A baryon sweep would thus indeed be dangerous to organic matter, for the reason stated above.
The first draft script of "Death Wish" contained a reference to proto-matter, rather than referencing baryonic particles.

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