When a person dies with more debts than assets, the court refers to this as an “insolvent estate.”
When this happens, you have a few options, none of which is that great.  

Option 1: Walk Away

First, you can do nothing. In Washington, heirs are not responsible for the debts of their relatives. So, even though a relative might have left large credit card bills, you have no legal responsibility to pay them. If, however, you place the relatives car in your name, then you have taken an asset of the person's estate that should by all rights go to the credit card company or one of the other creditors. It is not recommended that you take assets in such situations, except for possibly heirlooms, pictures or other assets that have little or no value other than to you and the family. Walking away can be difficult for people to do, but sometimes it makes the most sense.

Option 3: Negotiate 

Third, you can try to negotiate with the creditors. This can be tricky when you are not the court-appointed representative of a person’s estate, but creditors are sometimes willing to discuss the debt if you are family member, and you are willing to pay them off, even if at a discount. Getting a proper release from the creditor however is essential if you plan to pay off any debt. Once the debts are low enough that the estate becomes solvent, you can begin a probate that will allow you to get nonintervention powers or you can proceed without a probate using the process for Small Estates.

Option 2: Wait Two Years

Second, you can wait two years. Washington has a two-year statute of limitations for claims against deceased persons. Therefore, you could wait for two years after the date of death. After that, creditors can no longer bring a claim against the estate. During that time, however, creditors can file a probate to try to gain access to assets, although this is very rare. Also during that two year period, banks that hold the funds of your loved one may hold it, but may forward the funds to the unclaimed property division at the Department of Revenue. This doesn’t mean the property is lost, but must be accessed later, preferably after the two-year statute of limitations has expired. To check to see if the Department of Revenue is holding assets of a deceased person (or a living person), go to www.claimyourcash.org.

Option 4: File a Probate

Fourth, you can file a probate. The problem here is that the court will not likely grant you nonintervention powers. Therefore, ironically, even though the assets are usually minimal, the complications and expense are much greater than a normal probate that could have a lot of assets. By not having nonintervention powers, you must return to court anytime you want to do most anything related to the estate, such as pay bills, sell assets and close the probate. If you plan to proceed with a probate of an insolvent estate, you should first consult with an attorney.