Can my family bring a claim on behalf of a family member that has died?

Yes.  The Wrongful Death Act and the Survival Act allow for claims to be brought in the unfortunate event that a family member dies from an accident.  The Wrongful Death Act focuses on the damages to the family, for example the financial support and loss of society and companionship resulting from the death, while the Survival Act allows for damages for pain and suffering and other elements of damage to the family member from between the accident and their death.  This statute is used when a family member dies while litigation is still pending.  In that event, an estate is opened and the claim can continue to be pursued by the family.