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Thus, a person called to testify before Congress can refuse if they believe the government could use the testimony against them in criminal proceedings. To render the protections against self-incrimination ineffective, Congress can provide immunity from criminal prosecution.
Plaintiffs can choose not to testify in their own behalf -- as witnesses in the plaintiff's case. That would be strange, but it is not illegal. At trial, the plaintiff must go first and the plaintiff would need to prove up the case -- all elements of it -- by other admissible evidence if the plaintiff declines to testify.