Monday is the day when each department head in marketing activates his or her voicemail.
Everybody who hears little Loretta sing has his or her own way of telling her parents that she is expressive.
You know that "each department head" and "everybody" do actually refer to more than one person, but they function as singular nouns because of their wording; they contain special words such as "each" and "every" that make them act as singular nouns, thus requiring singular pronouns.
Sometimes, you can avoid an awkward-sounding singular pronoun by rewriting the sentence by using a simple plural noun and pronoun. For example: Monday is the day when the department heads in marketing activate their voicemail.
The following words make a noun or pronoun singular:
Use singular pronoun forms with these words. If the "trick singular" refers to a mixed-gender group, use "he or she" or "his or her" in order to be correct. ("They" moving from singular to plural is incorrect here.)