Relational query for universally quantified formula
SQL does not have a universal quantifier, but an equivalent can be constructed from the existential one, through a normalization process similar to Skolemization: $$\forall x P(x) \iff \nexists x \neg P(x)$$

In your case, you want the users for which there does not exist a book that they have not borrowed:

select * from people p
where not exists
  (select * from books b
   where b.id not in 
     (select book_id 
      from borrowings
      where people_id=p.id)
  )


(Note that I have assumed tables for people and books to represent their existence separately from the borrowings table, which, for instance, may be empty at the inception of the system.)