@Tiffany944 Yes! The guest needs to initiate the cancellation. Under no circumstances should you do so as you will face penalties.
I too have a strict cancellation policy and offer the same thing you do, which is a potential additional refund if any portion of the cancelled dates are able to be rebooked. I would send her a message stating something along the lines of the following
"HI XYZ, my apologies that you are unable to complete your stay. I would advise you to cancel the reservation as soon as possible, therefore my calendar will be opened again for potential bookings. In the event I am able to rebook any of your cancelled days, I will happily refund you that additional amount. Thank you so much."