Do possessive pronouns sometimes take the place of a noun?
They take the place of possessive nouns, but they cannot function as a noun.
Possessive pronouns such as his, mine, your, and its are used to describe ownership. They replace word's like Sara's, Bob's, or Macy's. However they never function as the subject.
For example, "Jackie's dog went missing." would be written as "Her dog went missing." While "her" replaced "Jackie's," it does not function as the subject, which is "dog." You wouldn't say "Her went missing." That would be considered a fragment because it lacks a subject.
All in all, possessive pronouns take the place of possessive nouns, but they cannot function as a noun.