What would happen if you slept on a bed tilted at 45 degrees?

If I am reading your question correctly, I would say that a 45 degree tilt is appropriate for some sleepers with back problems:

Adjustable beds work by giving the user flexibility in how the different sections of the bed are positioned. For users with back problems an adjustable bed can be a real life saver in allowing you to get a good night’s sleep. Typically the user will tilt the upper body portion of the bed to a slight incline from about 30 to 45 degrees. At the same time the section under the legs can be bent to give an angle under the knees. This combination of bent knees and raised torso can give the most comfort to back pain sufferers. The bent knee position in particular takes the pressure off the lower back.

http://www.freerepublic.com/focus/news/2726166/posts

This says 10-30' is optimal for circulation and other health benefits.

A surprisingly popular form of nightly rest in the Middle Ages, mostly with members of State and highly paranoid soldiers. Sleeping at a 45 degree slant (head up) allowed someone in deep slumber to spring into action should anyone attempt to sneak into the bedroom in the middle of the night and murder him.
King Charlemagne is said to have slept in this manner.

http://www.everything2.com/e2node/Sleeping%2520at%2520a%252045%2520degree%2520angle