Sure -- if their biology allows them to generate long chains of polymers.
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Modern "bulletproof" vests *(without additional hard ceramic plates)* are made of multiple layers of tightly woven synthetic fibers called [aramids][1].  They derive their strength from having multiple chemical bonds along the polymer chain, which are oriented along the axis of the fiber when it is drawn out.

It should be noted that while such vests will stop bullets, they can often leave a "dent" below them *(they're tested on clay dummies)* -- this can often result in injuries like a broken rib.

*(completing answer)*

[![how vests are made][2]][2]


Some vests have their layers of fabric additionally coated in a resin.

[![example of struck vest][3]][3]
  [3]: https://i.sstatic.net/nrUe3m.jpg


  [1]: https://en.wikipedia.org/wiki/Aramid
  [2]: https://i.sstatic.net/fDkLn.jpg