@Spencer8
If I understand it right, they were smart and didn't cancel. They changed the reservation which is possible before and during their stay. By accepting the change you agreed to it, so instead of a cancellation (even though in theory that is what they worked around). it is now technically a new contractual basis because you agreed to it. Payment will be made according to this new agreement and there is no basis for you to demand a refund.
This is what I have come to learn from multiple postings on the same topic. Of course, contacting Airbnb directly wil tell you for sure.
It doesn't seem fair to be able to circumvent the cancellation policy, yet it's a loop hole that clever guests have discovered, and there's nothing in the Airbnb clauses to prevent it.
It's always up to the host how to decide to handle such ammendments - accept the change or don't accept and open the door to retaliation.
You do also have some maneuvering space.
If for example you have a minimum booking of 2 days, but gave a guest a reduction for staying a full 14 days bringing the daily fee down from let's say $60 to $55, then that is an agreement on the basis of staying longer.
If they then send an alteration bringing it down to less than that period at $55 you could decline it and send an alteration from your side for the desired number of days at the normal price of $60 (plus of course any cleaning fee you might have) for them to accept.
I've also heard of guests trying to get around the minimum booking days this way by booking the minimum and then using a reason to ask the host to reduce to under the minimum.
If a guest for ex. booked my minimum of 2 days and then asked to change to only 1 day due to whatever reason, then that wouldn't be possible because my price calculation and day minimum being based on amount of work. Or I'd send them an ammendment to 1 night but for the price of 2. In order to do this I'd override the listing setting and change it to 1 night minimum until after the ammendment is sent off, then quickly change back to two.)