I shortened a stay at the SF Ren one time via 800#, & they were going to apply a higher rate because of the change (think the lower rate had sold out? don't know. it was a weekday rate but a really good one; I had booked it way in advance). They got a supervisor to ok the original rate. Of course when I got to the hotel they wanted to charge me the high rate, but I had the original printout showing the lower rate, the date/time I talked to 800#, & the name of the supervisor, so they honored it.
I know a lot of hotel chains are saying if you shorten the trip on the back-end you can face a higher rate or even a 1-night charge. Have seen that a few times. I've also had Hilton want to up the rate if I shorten a trip, both on the front & the back end.
Unlike Bruce, I've usually had good luck w/ Marriott when calling to shorten stay due to plane cancellation/weather where there's no way I can get in. I usually call & say hey I've got the reservation, believe me I'd much rather be w/ you than stuck on this plane or in this airport but they can't get me in until tomorrow, so would you please cancel tonight but keep the remainder of my reservation & I'll see you as soon as possible after the plane lands. They do, & I don't get a higher rate. In those instances btw, I call the front desk of the hotel & not the 800#.
Cheers.