California State Senator Sharon Runner has introduced SB 49, to give the Governor discretion to cancel special legislative elections if only one person files to be on the ballot. See this story.
Current law already says that a special election should be canceled if only one candidate files to be on the ballot and no one files as a declared write-in candidate. However, it is believed that there has been no instance of only one candidate filing for a legislative special election, and no write-ins filing either, at least back to 1967. Before 1967, California special legislative elections were non-partisan and had no party labels on the ballot. The existing law is in any event not functional, because the deadline for a write-in candidate to file is two weeks before any election, and it is logistically impossible to cancel an election within two weeks of the expected election date. The early voting period is four weeks before election day.
A handful of other states don’t hold legislative elections (regular or special) if only one person files to be on the ballot, but they are all states that either don’t permit write-in votes, or which set a write-in filing deadline months before the election. Those states are Arkansas, Florida, Hawaii, Louisiana, Nevada, and Oklahoma.