Sometimes, especially in comedies of the 80s/90s, there will be a character whose very purpose is to be made fun of for being unattractive - be they an "abhorrent admirer" where the joke is how the main character gets stuck with them or has to escape their advances, or, for example, a "fat woman" in Al Bundy's (of Married... With Children) shoe shop so Al can deliver a stinging remark about their weight.
How do the casters advertise these positions? Do they actually say they are looking for a person ugly enough to be the butt of a joke about their appearance?