What happens to a MacBook's battery once it reaches the maximum cycle count? I have a MacBook Pro and according to Apple, its cycle count limit is 1000. What happens when it surpasses 1000 cycles? Will the battery continue working or not? Will the MacBook still be able to receive power from the battery or not? Should it be replaced?

Thanks.
As it says on the page you've linked to (emphasis mine):

Batteries have a limited amount of charge cycles before they're considered to be consumed. Once consumed, a replacement battery is recommended. You can use your battery after it reaches its maximum cycle count, but you might notice a reduction in your battery life.
Knowing how many charge cycles your battery has and how many are left can help you determine when a battery replacement is required. For best performance, replace your battery when you reach its maximum cycle count.