I got curious about this so I decided to look into it.
The California Grizzly Bear became the official state animal of California in 1953 and is prominently featured in the California state flag. However, the California Grizzly Bear has been extinct since the 1920s. California is the only state in the union that carries the image of an extinct animal on its state flag and seal.
The California grizzly bear (Ursus arctos californicus) is an extinct population or subspecies of the brown bear. There were once as many as 10,000 California Grizzly Bears throughout California prior to Spanish settlement. The loss of habitat and over-hunting by a rapidly growing human population led to their extinction. Black bears are now the only wild bears in California.
The California Grizzly Bear first appeared on the the flag during the 1846 Bear Flag Revolt. The Bear Flag Revolt was a revolt by American settlers in Mexico-controlled California in 1846. Sonoma, California became the headquarters for the last remaining rebels, who created the Bear Flag. Independence of the California Republic from Mexico was declared on June 14, 1846 and the Bear Flag was raised over Sonoma.

California became a US State in 1850. The Grizzly Bear remained on the flag through various versions until the current flag was made official in 1953.


For more about the California grizzly bear see the video below from the San Bernardino County Museum.