Sort of. On those cruises that DCL deems as "not selling well" they may come out with last minute restricted fares after the paid in full date.
These fares, while lower than the prevailing rate at the time, do tend to be higher than the price for the same cruise was on opening day.
With the last minute fares, you book a type of room (Interior, Oceanview, or Verandah) and DCL will put you in a room of that type (or higher) dependent on what's available.
You must pay in full at the time of booking and there are no refunds, or changes allowed.
This is a really good thread to read for more specifics (from the stickies)
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