Can tonsil stones form after tonsils and adenoids are removed? wife has severe halitosis, great dental hygiene, non smoker, non drinker...

No: But anything is possible. Could be from GERD, gum infection, pet nasal drip, infected sinus, abscessed tooth, change in Meds or supplements, impacted food debris, etc. Start with a dental examination. Ask Dentist about tongue scraper. Let him/her do oral hygiene evaluation. If cause is not a Dental her Dentist will refer her to appropriate Physician to continue investigation.

Halitosis: Bad breath can also be caused by acid reflux, your diet, poor oral hygiene habits, cavities, and periodontal disease just to name a few. Brushing your teeth well may not do the trick. Have your dentist give you a thorough examination with a full set of radiographs and a thorough hygiene visit to rule out any dental problems. If none, consult with your physician about possible other causes.

Unlikely: In the majority of cases, the cause of bad breath or halitosis, is the product of bacteria in the mouth. Bad breath can be very embarrassing, but it is a common condition and there are numerous ways to treat it. See your dentist for Halimeter test, diagnosis and bad breath treatment that depends on its cause. Good luck.