Everyone has the ability to do some form of exercise even if you face some pretty intense bodily or otherwise limitations. For example if you are concerned with falling there are many balance exercises for people that can be done holding onto a chair or a doorframe. One of those exercises start with standing behind a chair while holding its back and lift one leg to about the height of the middle of the calf of the other leg while tightening your abdominal muscles. As you do it for longer and get better at standing on one leg you could leg go of the chair eventually and do it on your own.
Core strengthening exercises are possible to even if you have limited abilities. A plank is a safe way to train your core and one that does not involve much risk of any injury. Usually a plank is done holding yourself parallel to the floor with only your forearms and toes touching the mat. However there is another form that can get you started if you cannot quite get there, you can instead plank while standing and leaning forward onto a desk, table, or wall with your elbows and forearms while resting on the balls of your feet with your back straight.
There are also basic stretches that you can do while laying down on your back and just fully extend your legs and arms to stretch them, as simple as it sounds. There are also many exercises that you can do from a seated position, bicep curls, knee extensions, and shoulder blade squeezes to name a few.