Your confusion is arising from the fact that you think a foreign key is a modified version of a primary key. It is not, it is a separate item.
For instance, CustomerID in the Customers table would have a primary key, but CustomerID in the Orders table would be a foreign key referencing (pointing back to) the primary key in the Customers table.
In the Customers table, the primary key serves to uniquely identify each customer. In the Orders table the foreign key on CustomerID serves to guarantee that each order belongs to an existing record from the customer table.
You can have the primary key without establishing any foreign keys, it will still serve it's role in identifying records. But you cannot have a foreign key without a primary key in a different table (or, in rare occurrences, in the same table) because the primary key name is part of the definition of the foreign key. And you can have as many foreign keys as you want in different tables (in rare cases in the same tables) pointing back to a single primary key.