The sand used for the core is generally different from the sand for the rest of the mould.
Core pieces are made up, sometimes baked, and then suspended inside the cavity. Easier to do if you can suspend the core in more than one place.
After casting and cooling the flask is dumped, the green sand broken off and oil added for future use. Then the core is broken up - sometimes not easy, it takes some work to get it all out. The core sand is not reused to my knowledge.
There is a foundary in the town where I work - half owned by Ford - that makes exhaust manifolds, transmission housings, differential housings and such. They have some wonderfully curved and intricate cores and moulds. Production line. 3 pots of iron - each 10-12' in diameter and about that deep. Quite and event when the pour. Dirty filthy work - they go at it 8 hour shifts, 3 shifts a day, 7 days a week. Shut down 2 weeks every 6 months and maintenance folks replace every motor they have time for. Makes me enjoy being able to cast bullets once a week or so.