Yes, they can, and occasionally they do. You may be able to demand a refund, but that won't help make your trip work. This is a very good reason to buy travel insurance. When (post Cyclone Pam) Air Vanuatu changed our trip by 2 or 3 days, I was able to get them to only change it by one day (no charge of course) and the travel insurance covered the extra night in the Vanuatu hotel. I was lucky that the next hotel I was going to just agreed to a later arrival date, even though that brought me under their minimum stay, but if, for example, they had insisted on being paid for the original night I booked and didn't use, the travel insurance would have covered that too.
If changing the date makes the trip just not work - for example you won't arrive in time for the event you are going to - then talk to your insurance company about whether you can book a different flight that does work, and claim for the cost. This wasn't an option for us because Air Vanuatu was the only airline flying between Vanuatu and Fiji and they were not running any flights on the day we had originally booked (they do 2-3 flights a week between those points.)