In case you needed another reason to ensure your email gets shut down after your death, check out this story about a woman whose email account was hacked two years after her death, following which the hacker started spamming everyone in her address book.
Most webmail companies have policies on closing down email accounts after the owner’s death. I strongly recommend investigating how your webmail closure system works and making sure both that you have an authorization in your will to deal with your digital life and also that whoever will be managing your estate knows that you want to have it closed down.