Let's say that you've followed tips 1-4, and the claimant still won't go away. What choices do you have? There are two, really:
1. Settle; or
2. Go to trial.
Tip #5 is to try and settle the claim.
When real life people have debt, it can be a big pain. You are, in many ways, at the mercy of bill collectors. If you fail to make a payment, they can ruin your credit rating, making it difficult for you to rent or purchase a home (or, perhaps, get a job). They can also be an incredible nuisance, calling at all hours of the day.
By contrast, dead people (or their representatives) have a number of advantages over creditors:
a. They don't care about their credit rating -- it's irrelevant.
b. Wherever you go when you die, I doubt you receive calls from bill collectors.
There's also the advantage of time, which is usually seen as a disadvantage but may be a real asset. Most creditors want their money ASAP. But most creditors understand enough about probate to know that the release of funds takes time. That makes them willing to accept much less than the amount owed if they can get the money right away. For instance, a credit card company with a claim of $10,000 may be able to accept $7,000 or $8,000 (or even less) if they can receive payment ASAP. There's only one way to find out, and that's by asking for a discount. The worst thing that can happen is the creditor tells you "no."
One final note: if you do settle for less than the value of the debt, the difference between the debt amount and the settlement amount is income to the estate (as forgiven debt).