Teeth bone does not grow back on it's own.
However a dentist can regenerate the teeth bone through dental teeth bone regrafting.
So while the teeth bone will not and cannot regenerate on it's own and grow back on it's own once the bone has been lost or cut out etc the dentist can bring the bone back through grafting.
Your teeth bone surrounding your teeth can be regenerated through regenerative grafting in order to optimize the bone support and keep your teeth in place.
The teeth bone can also be regenerated after losing your teeth in order to place dental implants to replace and restore the missing or lost teeth.