It happens fairly frequently, because a very large number of criminal acts can also result in civil liability and/or affect one's rights in a divorce, probate, etc. If a defendant does not want to testify in a civil case due to potential criminal liability, he is free to refuse to testify. However, he has to accept the fact that the judge in the civil case will assume he had nothing helpful to say for himself and likely rule against him.
Examples that come to mind from my practice are:
(1) Three defendants in a civil case for theft of their employer's property, who refused to testify due to an ongoing criminal investigation for the same acts. The judge presumed that the answers they refused to give would have been admissions, and granted judgment in favor of the employer.
(2) An heir in a probate case was accused of having killed the decedent, which would mean he could not receive his inheritance. He refused to answer any questions about the alleged murder, and the judge disinherited him.
