Core1 would send a invalidation to get exclusive (write) access to that cache line. This would be routed to Core2. Which removes the cache line from its cache.
If core2 now accesses that cache line again, it would not find it in its L1, or L2, and at L3 there is the cacheline directory routing the request to core1.
If core2 now accesses that cache line again, it would not find it in its L1, or L2, and at L3 there is the cacheline directory routing the request to core1.