A bear appears on the Coat of Arms of the Rosenberg family. Live bears have been kept in the castle moat since 1707. Currently 4 bears are held.
See www.atlasobscura.com

The "Bärengraben" is currently just outside the WHS boundaries on the far side of the Aar. "The first bear pit was at what is still called the Bärenplatz (Bear Plaza). The current pit is the fourth such enclosure, following on from pits at various locations around the city, and was first opened in 1857." See Wiki for story of how the bear became the symbol of the city.
See en.wikipedia.org

The city's coat of arms portrays the bear which was involved in its foundation myth and the Transfiguration Monastery keeps a caged specimen to represent this. The current bear is called Masha.
See www.strangetrue.org