Some of the absolute basic exercises that should be performed if you are bed-bound include ankle pumps, heel slides and rolling from side to side to change position. Doing these exercises regularly several times a day will help from developing blood clots, pressure ulcers or bedsores, and contractures (shortened, tight muscles).
Stacked breathing is a technique to increase the size of the breath you are able take in. It can also improve the strength of your voice and your cough, so you can better clear out the lungs, as well as your lung flexibility.
Squats are a very useful exercise to make it easier to get up from a chair, off the toilet and out of bed. If this is difficult, try the sit-to-stand variation first or if too easy, do the supported squat variation instead. It can also be helpful if you have one-sided weakness, like after a stroke.