If Homer Barren in "A Rose for Emily" represents the unwanted North, then why does Emily desperately cling to his corpse, as if she needs him?
In William Faulkner's "A Rose for Emily" the character of Homer Barron represents more than just the unwanted North, as your question states.
Homer does represent the unwanted North in terms of his rash behaviors, his nonchalant ways, and his treatment of men and women alike. However, he also represents the very essence of rebellion that Emily has been forced to repressed as a woman growing up and living in the South. Everything Homer does causes a revolt in the town and in Emily's close relations. He represents everything that Emily's dad would have forbidden.
This being said, we really do not know what Emily's thoughts are throughout the story. We only see her reactions. We do not know if Emily resents the teachings of her father, or whether she agrees with his imposing ways or not. All we know is that she lacks the ability to confront reality, that she is a follower, that she allows men to be in control of her, and that she hates to be alone.
When she clings on to Homer's body after he dies she is not clinging to a representative of the unwanted North. She is clinging to a man that represents her suppressed rebellion against a suppressing society that is now changing without her control. Homer is to Emily the last resort to ensure that her life has not been completely wasted. No matter how good or bad he is, he is the only person with whom Emily could share whatever her life has become. Losing him for good would be losing that little bit of life.