What is the privilege against self-incrimination when a witness has been granted immunity from prosecution?

the privilege against self-incrimination, since generally, "where a witness receives immunity, that witness's testimony is compelled and the witness no longer has a privilege against self-incrimination. [Citations.]" (People v. Morgain (2009) 177 Cal.App.4th 454, 466-467.)

In People v. Hathcock (1971) 17 Cal.App.3d 646 (Hathcock), on which the trial court primarily relied, a murder occurred. Sometime later, Hathcock, who was the wife of one of the murder suspects, was granted immunity pursuant to section 1324 from prosecution for any offense arising from the murder. She thereafter gave a written statement to the district attorney implicating her husband in the killing. She also testified for the prosecution at her husband's first trial, which ended in a mistrial. At the second trial, she again testified for the prosecution and implicated her husband; however, when asked if she had truthfully told defense counsel her husband was not involved, Hathcock stated she could not answer the question because she would have a perjury charge if she did. Hathcock ultimately testified she knew her husband had not done it, because he was not there. Based on this last answer, she was prosecuted for, and convicted of, perjury. (Id. at p. 648.)