This girl came to me when she was 7 years 9 months old with a thumb sucking habit that she was not able to get rid of by herself. She had an anterior open bite (her upper and lower front teeth did not overlap vertically they way they are supposed to) and her top teeth were too narrow.
We decided to use a fixed (attaches to braces on the upper molars and stays in all the time) habit breaker to help her eliminate the habit. Despite having the habit breaker in, she continued to suck her thumb. After trying for more than 6 months with the fixed habit breaker, we decided to work on the width of her upper arch with a removable appliance (also with loops embeded in the acrylic as per the fixed appliance). After over three years, she finally stopped her habit.
The following photos were taken at age 12, before her braces were put on. The only appliances that she had up to this point were the habit breaker and a removable appliance to correct her narrow upper arch. I did not do anything to specifically bring her upper and lower front teeth together. This happened spontaneously after she stopped sucking her thumb.
This woman had a thumb sucking habit up until the age of six. Her open bite persisted despite stopping the habit. These photos were taken at age 23.