Maybe. It is impossible to give a firm answer without a lot more information.
If the witness is subpoenaed for a preliminary hearing -- which is a proceeding in felony cases only to determine whether there is enough evidence to proceed to trial -- the District Attorney can have a police officer testify about what the witness said.
If the witness received a subpoena for trial but does not appear for court, the District Attorney can ask for a continuance and ask for a body attachment, which is like an arrest warrant. The witness could be taken into custody and held until the trial can be held.
The District Attorney may also decide to proceed to trial without the testimony of the witness, and attempt to introduce statements the witness made to the police through an exception to the hearsay rule. It is usually very difficult for the prosecution to introduce statements as evidence over the objections of the defense, but it depends on the situation.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like Avvo, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
I agree with Attorney Marshall's answer. Basically if it is a misdemeanor case, if he/she doesn't show up and they can't prove the case with other evidence, then probably dismissed if there is a no-time waiver status, or it will be continued if time is waived (ask your attorney about these terms).
If it's a felony, then depends on the same facts and whether you are talking preliminary hearing or trial. If dismissed once, they can still bring the case one more time.
Finally, if the witness was subpoenaed, but doens't show up there are some ramifications for the witness potentially.
Final note - don't get caught tell the witness or causing the witness not to show - leads to BIG trouble.
In addition to the answers provided by the above attorneys, you should know that if the witness in question is the victim, and the victim appears but refuses to testify, then the court may hold the victim in contempt. However, unlike any other type of witness who refuses to testify, a domestic violence victim who refuses to testify cannot be incarcerated.