Serious conduct frequently produces a criminal investigation, a regulatory enforcement action and private civil litigation at once. Defending them independently is how a defence loses.
The Fifth Amendment problem. An individual who invokes in a civil case may suffer an adverse inference, which is permitted in civil proceedings though not in criminal ones. A company cannot invoke at all, and its inability to produce a witness because the relevant individuals are invoking is a recurring difficulty.
Stays. A defendant may seek to stay civil proceedings pending resolution of the criminal case. Courts weigh the overlap of issues, the status of the criminal case — indictment materially strengthens the request — the interests of the plaintiff, the court and the public. Partial stays limited to depositions are a common compromise.
Information flow. Discovery obtained in a civil case can be shared with criminal authorities, and government agencies share among themselves. Everything produced anywhere should be produced on the assumption that all three forums will see it.
Sequencing. Settling the regulatory matter first can produce admissions used in the civil case; resolving the civil case first can leave restitution credited in the criminal one. There is no general rule, only a decision that must be made deliberately.