You should state the reason for not using implants in the first place. There are surgical solutions of different kinds, ranging from the Edlan-Mejchar technique of vestibular fornix extension to advanced forms of hard/soft tissue grafts. There are also prosthetic options such as sub-mylohyod retention. Should you have a particular case in mind, please do provide some details to allow the opening of a discussion on the topic.
We would be happy to review your CT data and 3-D imaging of your patient with the severely atrophic mandible to amke recommendations for implant supported prosthodontics.