Constipation is unfortunately a very common problem in the elderly. Also unfortunately, it can cause some serious problems with longstanding bowel damage if it becomes severe. I would recommend discussing your concern's with your mother's doctor
as this should be addressed.
In general, it would be rare for not eating enough to cause constipation. It is possible, as can only excrete waste if there is food to create waste--but rarely is someone eating so little to develop constipation. If she is maintaining her weight, this is unlikely to be the cause. Keep in mind, constipation is medically defined as less than 3 bowel movements a week...that is, everyone does not need to have a daily bowel movement. However, if she is having abdominal pain
or the feeling of fullness--regardless of how often she has a bowel movement--she should see someone.
The more common cause of constipation is not how much, but what food she eats. As you point out, fiber is an important part of bowel health. It is difficult in the modern day to get adequate amount of fiber so fiber supplements are a good alternative. While it would be better to eat fiber enriched foods (vegetables, beans, grains), there is no reason she could not take a fiber supplement as a long term solution. There are many types of fiber supplements on the market--hopefully she can find one that she does not mind taking.
I would discuss this further with your doctor. There are medical and dietary causes of constipation that should be ruled out to ensure there is no serious problem developing. Good luck.