1) If the Marine had a will and the executor has properly filed the will, then the executor can assume control of the account with appropriate documentation. I assumed control of my brother's AOL account (although that took some money) and was able to wind it down.
2) If the Marine was intestate (did not have a will) depending on the state, an administrator (usually with the Next of Kin preferred) can be named executor or administrator of the Estate. Then #1 can kick in.
Essentially it boils down to sort of a business proposition. I'd be surprised if Yahoo did not have some policy regarding deceased accounts. An executor/administrator is empowered to act on behalf of the estate of that person which would even include free email accounts.
I was the executor of my mother's estate several years ago. And I believe (but cannot confirm) that Yahoo!'s publicly-stated policy on the contents of email boxes is that they get zapped when they receive documentation that the boxholder has died. IANAL and YMMV.
You've all given me more things to thing about if and when my son, a Marine, goes back to Iraq. First of all, they all spend time filling out lots of "in case of death" papers--at least those in my son's company do. They make them out before they go. However, it never crossed my mind to ask him for passwords. Well, one more thing to add to the list.
But death law varies by states.
Also, Yahoo! provided a free service, unlike AOL.