Most vegetables are pretty low in calories and they are healthy for you as well.
So you could eat many vegetables and yes you can eat unlimited amount of vegetables to keep you feeling full and you can still lose weight.
Vegetables are a good choice for food when losing weight but just avoid starchy vegetables as they may increase your weight if you eat too many of them.
I ate mostly vegetables when I was working on losing weight and I ate quite a bit of vegetables to keep my stomach full and to have energy and I still lost 100 lbs in a year.
I also exercised by walking, jogging, hiking, running on a treadmill using an exercise bike and even riding my bicycle.