Many similarities exist between natural sleep and anesthesia.
During early parts of natural sleep, an individual is difficult to arouse. During general anesthesia, a patient cannot be aroused. Parts of the brain that are responsible for sleep are similar to areas that control general anesthesia.
When one type of anesthesia, propofol, is used and there is natural sleep debt, it dissipates. Specifically, a REM sleep deficit was apparent after exposure to isoflurane, sevoflurane or halothane and a NREM sleep deficit is seen after halothane.
Controversy and dangers concerning prolonged and daily use of propofol
Propofol administration to achieve the recommended level of sedation suppresses the REM sleep stage and further worsens the poor sleep quality of these patients.
http://icmjournal.esicm.org/Journals/abstract.html?doi=10.1007/s00134-012-2623-z
http://edition.cnn.com/2013/06/21/showbiz/jackson-death-trial/index.html?hpt=hp_t1