A U.S. passport is basic identification that is necessary for international travel. It can also be a souvenir of your journeys, as all of those stamps and visas serve as reminders of past vacations. When a relative passes away, you may want to keep that person's passport as a memento of your loved one's travels. Having a document with your relative's photo and signature may be comforting, and it could be a helpful addition to your family history records.
In the United States, you can legally keep a deceased relative's passport. The website U.S. Passport Service Guide quotes the National Passport Information Center (NPIC) as saying it is legal to simply do nothing with such a passport. NPIC is the call center for the Department of State's Passport Services. Just hold on to the passport and keep it safe. Until it expires, it is still possible for someone to steal it and use it fraudulently.
If you're more worried about security than nostalgia, you can mail in the passport of a deceased relative for cancellation. Send it to the Consular Lost and Stolen Passport (CLASP) unit of Passport Services. The address is: Attention CLASP; 1111 19th St. N.W., Suite 500; Washington, D.C. 20036. Include a copy of your relative's death certificate and a letter requesting cancellation of the passport.