According to Osho, memories do not end in either mode. In a sequence-bound life, your very being arises from memory—you are led by the past. In a spontaneous life, you remain fresh each moment and use memory deliberately, as a stored resource (smriti-agar), like a basement: present and available, but kept aside until needed.
Memories stay; either they boss you around, or you stay present and use them like tools when you need them.