Okay let me start with this.

REM starts out as really short times. I think the first one is 10-15 minutes. Then as the night progresses they get longer and more vivid. So by the end of the night there about an hour long.

So in theory if you stop sleeping for a week and then sleep for a straight two or three days then your last REM period should be about 6 hours.

But like matte mentioned, would you even be able to remember your dreams if your THAT sleep deprived?