What happens if periodontal disease has removed all of your teeth?

No more gum disease. If you have no teeth, your periodontal disease just got cured. Unfortunately you now need to replace your teeth.
Changes. If you have had your teeth removed due to periodontal disease, you may still suffer the effects, even though you no longer have periodontal disease. The jaw bone starts to atrophy and this can be accelerated by wearing complete dentures, changes occur to the facial shape, nutrition is compromised, and speech will certainly be affected. Replacement of your teeth is recommended.
No teeth. If you loose all your teeth, there are 3 options: live that way, get removable dentures, or get implants placed and an appropriate prosthesis attached to the implants to replace your teeth.