All stars but one can be associated with an IAU constellation. IAU constellations are areas of the sky. Although there are only 88 IAU constellations, the sky is actually divided into 89 irregularly shaped boxes as the constellation Serpens is split into two separate sections, Serpens Caput (the snake's head) to the west and Serpens Cauda (the snake's tail) to the east.
The only star that does not belong to a constellation is the Sun. The Sun travels through the 13 constellations along the ecliptic, the 12 of the Zodiac and Ophiuchus.
Among the remaining stars, the nearer ones exhibit proper motion, so it is only a matter of time before some of them cross a constellation boundary and switch constellations as a consequence. In 1992, Rho Aquilae became the first star to have its Bayer designation "invalidated" by moving to a neighbouring constellation—it is now a star of the constellation Delphinus.
^Hirshfeld, Alan; Sinnott, Roger W.; Ochsenbein, François; Lemay, D. (1992). "Book-Review – Sky Catalogue 2000.0 – V.1 – Stars to Magnitude 8.0 ED.2". Journal of the Royal Astronomical Society of Canada86: 221. Bibcode:1992JRASC..86..221H.
The Astronomical Almanac (2000).
Roy L. Bishop, ed., The Observer's Almanac 1991, The Royal Astronomical Society of Canada.
Burnham's Celestial Handbook: An Observer's Guide to the Universe Beyond the Solar System, Vols. 1, 2, 3 (Dover Pubns, 1978).