In my experience, it's not unusual, though not common, for people (usually parties) to refuse to testify in a civil case based on the 5th amendment. The other side can ask the court to draw an adverse inference from this. I know an aggressive litigator who sometimes has his clients do this. He says "you won't win your case with your adverse inference."

That may be true, but the 5th amendment seems like a risky civil strategy to me. Usually the other side won't be entirely dependent on your testimony to prove their case. There can be other evidence out there that you might want to explain with your testimony, or you may otherwise wish to make your case with testimony.

It's worth knowing that in a civil case the 5th amendment is much less powerful and has risks as well as benefits.