If a falsely accused person dies, can their family face legal issues?

If a person falsely accused in a case has passed away, and their family is extremely poor, resides in another state, lacks legal knowledge, and is afraid to travel, could they face any legal issues in the future? Can the police or court take action against them even though they have no connection to the case? The family has never been contacted by the police or court regarding the case. If they do not submit any documents, such as the death certificate, could this create problems for them later? Is it their responsibility to officially inform the police or court about the accused's death, or will the case automatically close once the person has passed away? Additionally, if the family has no information about the case—whether it involves an FIR, a complaint case, or another legal proceeding—what steps should they take to clarify their situation and protect themselves legally?