Essentially, the answer is that there will have to be a personal representative (also sometimes referred to as an executor or administrator) of the deceased defendant's estate appointed by a court of competent jurisdiction, if a personal representative doesn't already exist, to enable any litigation of your claim to be started or completed. In short – the death of the party at fault is a significant complicating factor, so if you don't have an attorney yet on your personal injury case, you should contact one.
Now, for the longer, and more “legalese”, explanation. If a lawsuit has not been started yet, the insurer for the deceased party at fault may be willing to continue to deal with you or your counsel, and resolve your claim with you if you can negotiate to a fair settlement, despite the fact that their insured has died. However, if the insurer doesn't offer enough for you to feel that your claim should be settled, you will need to file a lawsuit. That is when the fact that the party at fault has passed really becomes an obstacle to proceeding, unless appropriate steps have already been or are taken.
In Washington, two statutes of interest are RCW 4.20.046 and RCW 4.20.050. Under RCW 4.20.046, subsection (1) essentially provides that all causes of action by a person against another shall survive to the personal representatives of the former and against the personal representatives of the latter; and subsection (2) provides that an action to recover damages for injury or death may be maintained against the personal representative of a person who would have been liable therefore but for his or her death. Under RCW 4.20.050, no action shall abate by the death of a party, but the court may at any time within one year thereafter, on motion, allow the action to be continued against his or her representatives or successors in interest. Finally, if the case is already in litigation and the defendant dies, CR 25(a)(1) notes that if a party dies the court may order substitution of the proper party.
In Oregon, the law is similar. The primary governing statute is ORS 12.190(2), which in pertinent part states:
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(2) If a person against whom an action may be brought dies before the expiration of the time limited for its commencement, an action may be commenced against the personal representative of the person after the expiration of that time, and within one year after the death of the person.
So, again, under the law of both Washington and Oregon, the death of a defendant will require that your personal injury claim be prosecuted against the personal representative of the party at fault that caused your injury.
The take-away from all of the above legalese is that the death of the party at fault can impact the cost of litigating your case, and it also triggers time deadlines and considerations that may be a trap for the unwary. Thus, if this situation is one that applies to your case, and you are not yet represented by counsel, you should seek advice on your case from a law firm that is experienced in dealing with such situations as soon as you possibly can.