What is the role of the described person in Shakespeare's "Shall I Compare Thee to a Summer's Day?"
Sonnet 18 is a sort of back-handed comparison of his beloved to a summer's day. He questions first whether the comparison ought to be made: "Shall I compare thee to a Summer's day?" He then goes on to list the reasons why the comparison cannot be made: the beloved is more "lovely" and "temperate"; no rough winds shake her buds of youth; summer is "all too short"; the skies are all "too hot"; summer's sunny "gold complexion" is often dimmed; the fairest weather fades; nature's course is changeable. He concludes that a comparison cannot be made because: "But thy eternal Summer shall not fade." Herein is one of Shakespeare's double-play on language. First, the implication is that the beloved's "Summer" shall not fade because the beloved is, along with being lovely, temperate in disposition, not moody like wind or a short season, not angrily hot, with an unfading complexion, and not changeable in the course of love and behavior. Second, Shakespeare employs a favorite convention in asserting that the beloved cannot be compared to short-lived, changeable summer because of the eternal longevity given in the poem. The end result is that the role of the beloved in Sonnet 18 is to live eternally as one who is more fair, lovely, dependable, and beloved than highly vaunted though changeable short-lived "Summer."
If I understand your question correctly, then the role of the described person is completely passive. While she is the object of the poem, she is just that -- an object.
In this poem, the described person does not do anything at all. She is just there and she is only there in the way that Shakespeare is describing her. While she will be famous, he says, it is not for anything that she has done. Instead, she will be famous only because he has written about her.
So I think that the role of the described person is very passive -- sort of like the role of a model who poses for a painting, perhaps.