While it is possible that the at-fault driver could face criminal charges (such as vehicular homicide, for instance), criminal matters are heard in criminal court. The state brings the case against the driver, and the penalties can include jail time, fines, and more. Not all motorists who cause fatal accidents will face criminal charges.
A wrongful death lawsuit will be litigated in civil court, which is separate from criminal court. In civil court, the “penalty” is exclusively financial. If you succeed, a judge or jury will award you a sum of money to cover your damages.
The criminal and civil cases are entirely separate matters. A civil wrongful death claim could be successful even if the at-fault driver is acquitted on criminal charges or never charged in the first place.