If your mother becomes incontinent, will the community advise you that she must be removed?
Incontinence in an animal may signal a curable condition or a correctable behavioral problem; I
suggest that your mother's canine companion be taken to a veterinarian who will be able to advise. Correction might involve something as simple as walking the dog more frequently. If it turns out to be an incurable incontinence due to aging or a neurological condition, diapers or a dog litterbox are options; see handicappedpets.com. Check with animal rescue organizations in your area; it is likely that at least one will have volunteers who work with elders and the disabled to help them keep their animal companions. Volunteer assistance with additional walks, diaper management, dog litterbox, etc., might be an option. The human-animal bond, especially between an elder and a longtime pet, is valuable enough to your mother's health to invest some effort in making it possible for your mother to continue to keep her companion. Leaky people aren't peremptorily discarded; leaky critters shouldn't be, either.