Yes - ships sail 'FULL' just like airlines these days - esp during holidays and high seasons. Prices come down if a particular sailing isn't selling. Many lines have a crew/staff privilege where friends & family can sail on standby and if there actually are available cabins, those get filled up. I've known of several instances where someones parents have flown a long way just to get left at the pier.
They will keep an emergency room for illness quarantine/bedbugs/domestic problems/technical issues in a cabin, but it's usually going to be a regular inside cabin.
Also - people cancel or don't show, so even a cabin empty on day 1 might have the occupant join the cruise 'downline'. There are often people who don't realized how small the average cabin is and book 4 people into a shoebox ;-) and then go to the guest services desk asking for another room to 'expand' into.
On my ship - even the crew cabins have often been 'full' and joining crew turned away at the gangway because there's absolutely no bed in crew or guest area to berth them.