Sure -- if their biology allows them to generate long chains of polymers.
--------------------------------------------------------------------

Modern "bulletproof" vests *(without additional hard ceramic plates)* are made of **multiple layers of tightly woven synthetic fibers** called [aramids][1] -- aromatic polyamides.  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.  Some vests have their layers of fabric additionally **coated in a resin**.

[![example of struck vest][2]][2]
  
It should be noted that while such materials will stop bullets, the impact will often leave a "dent" below them *(they're tested on clay dummies)* -- this can often result in internal injuries like a broken rib or heavy bruising.

Silk is a well-known example of a naturally occurring polyamide, renowned for its tensile strength.  [Experiments with multiple layers of silk serving as bullet-resistant garments][3] were done in the late 19th century, and they had some success in stopping low-velocity rounds.

The damage done to this material is not "spot"-repairable, so your creature would have to shed the entire damaged layer and regenerate fresh ones beneath *(I am reminded of birch trees shedding their bark as a parasite-resistant technique)*.


  [1]: https://en.wikipedia.org/wiki/Aramid
  [2]: https://i.sstatic.net/nrUe3.jpg
  [3]: https://en.wikipedia.org/wiki/Bulletproof_vest#Industrial_era