Can we add a primary key to a weak entity?

Question

I've learned that within a weak entity, each occurrence can't be uniquely identified using any available attributes within that entity. In other words, each occurrences can't be uniquely identified since there is no primary key.
All the textbooks and online materials give a solution to this by saying that we can uniquely identify each occurrence only through a relationship with an owner entity's primary key.
My question: Is it possible to just add a primary key to a weak entity?
then, a weak entity becomes a strong entity and we don't need to go through an owner's entity to uniquely identify each occurrences within a weak entity.