The theme of Family is interesting because we don’t hear about it directly, but we know it has to be there. Family is (hopefully) a big part of a deathbed scene in "I Heard a Fly Buzz When I Died." When Dickinson talks about the "Eyes" around the dying speaker, we have to imagine that these are her loved ones. Also, she gives away her "Keepsakes." That ritual of leaving a will is all about family and friends. We can’t assume too much about who these people are, but the idea of the bonds of family is a big part of what holds this poem together.
Dickinson refers to the people in the room as "The Eyes around," rather than naming and describing them. By doing this, she emphasizes the distance between the speaker and her family and friends.