When a 99 year lease expires the lease is just like any other 1 to 10 year lease when it expires.
Most places do not recognize 99 year leases legally anymore.
However when a 99 year lease expires and the person or family has been leasing the property on that 99 year lease then they must renew the lease again to stay on the property.
Just like when you sign a regular lease you either have to leave the property or renew the lease when the lease expires.
Most leases are for way less than 99 years now because the law does not make the 99 year leases legal anyway.
99 years is a long time and most people who sign a 99 year lease would die way before the lease is up anyway.