@Alissa95
It just sounds to me that these guests are trying to bypass the cancellation policy. For long term, if they are already checked in, the 30 nights from the cancellation date are non-refundable, not the 30 nights from the check in. So, in theory, they are supposed to pay for the nights they stayed PLUS the following 30 nights.
What is their reason for cutting the stay by so much? Did they complain about anything? Did something happen which is out of their control, e.g. an extenuating circumstances, or did they just have a change of plans?
I would factor my decision based on the circumstances, but no, you should not agree to the date change as you'll be completely out of pocket unless you get the dates rebooked and there's no guarantee with a last minute cancellation. I would tell them they need to cancel the stay and then you can offer to refund them extra ONLY if dates get rebooked.
If you do decide to allow the date change and have a long term discount, make sure you factor that into any refund you give, i.e. do not over refund the guests. If they only pay for a few nights, they do not get the monthly discount anymore and need to pay full prices for those nights. Deduct the difference from the refund by adjusting the price in the alteration request.