So what happens if the target of a grudge expires for unrelated reasons?
It's tricky. If you can claim even a
little of the credit - say, if they die in a battle and it may be that they were ill-prepared for that battle because not too long ago you tried and failed to claim vengeance against them - then it can be acceptable to consider the matter closed. It's not quite properly avenged, and it's not a victory you'd toast and celebrate, but it does mean the Grudge is no longer a constant itch at the back of your consciousness.
Otherwise, it could be inherited. If the Grudge is against a Warboss and they die to non-Dwarves, it's normal to consider whoever takes over the Tribe as the inheritor of the Grudge. This only flies for those who are not worthy of even basic respect - greenskins, Skaven, chaos tribes, and so on. If it's someone that does deserve basic respect, like a human or a Halfling, then it depends on the nature of the Grudge. If it's over the personal actions of that individual, then the matter dies with them. If the person holds a position of authority, then that institution could inherit the Grudge unless they disavow that person's actions and make restitution. If it's about property, then just as property is inherited, so are debts and Grudges - though courtesy would demand you let the inheritor know of the matter, and give them the opportunity to make things right before you resort to vengeance. For grey areas, consult your Clan's Elders, then your local Cleric of Grimnir, then your King. If all else fails, make a pilgrimage to Karak Kadrin and seek the wisdom of the Slayer Keep.
If the Grudge is against a fellow Dwarf, then first you talk to them, then your Clan Elders talk to their Clan Elders, then your King talks to their King, then escalate to the High King for him to adjudicate. This series of safety valves mean that as Grudge-happy as the Dwarves are, it's actually very rare for Dwarf-on-Dwarf Grudges to develop.
There's a few points where this breaks down. What if you don't know who did it? Elves kill a trading caravan, what do you do? History would suggest your King sends an envoy, but if the other party doesn't feel like being helpful things will spiral rather disastrously. This doesn't apply to the world's nastier denizens - if you don't know which greenskins did a thing, but you do know it was greenskins, then just get your vengeance on whatever greenskins are convenient, then double up just to be safe.
What if you have no idea who did it, and there's no way to find out? Pray to Grimnir for a sign and hope he gives you a clue. Failing that, you're stuck. Some will be unable to live with a Grudge they don't even know who to avenge it against, and take the Slayer Oath and seek death in battle so the impossible Grudge dies with them. Some will take the advice of the Cult of Grimnir, often travelling to Karak Kadrin for that purpose, to salve your conscience. If you don't know who ambushed your caravan, you might not ever be able to fully avenge the Grudge, but you can go about the rest of your life with survivable levels of shame if you, say, do your best to make sure others can travel that route safely. If you're a Warrior, join the patrols. If you're a blacksmith, arm caravan guards at cost. If what you do isn't immediately applicable, then the money you earn could pay for those patrols, or be donated to your local Temple of Grimnir.
What if the concept of death doesn't properly apply? If Konrad von Carstein killed your son but then got shanked with a Runefang, there's nothing you can do to pursue vengeance but the Grudge lingers because chances are he's not permanently dead. This is part of what made the Drakenhof campaign a big deal - all those Grudges could have been stuck in limbo forever.
