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HelloThis is Samuel. Even as a party in a civil matter, the 5th Amendment is going to apply. That means you can take the 5th and not testify if called upon by the other party. No one in any situation is mandated to provide self-incriminating evidence.
In civil actions, however, there is no prosecutor on hand. The issue then shifts to whether "the claimant is confronted by substantial and ‘real,’ and not merely trifling or imaginary, hazards of incrimination." Marchetti v. United States.
Because the privilege against self-incrimination applies only in "instances where the witness has reasonable cause to apprehend danger" of criminal liability, the deposing lawyer should assess in advance, in light of what counsel knows about the case, whether the witness has a realistic basis for such a fear.
If the party is going to testify, they should place their name on the witness list. That way the other party can decide what and how much discovery they want to do.