Is it true that teeth move and shift over a period of years?

Yes: This is true. Teeth can shift eventually causing the bite to collapse. If there are any missing teeth then you should really replace them.

Yes: Teeth can shift for many reasons including wisdom teeth growing in, clenching, grinding, diseases of the gums and abnormal growths within the jawbones. If your teeth are moving/changing, see your primary care dentist who may then refer you to a more specialized provider, if necessary.