In the situation you have described, it will only be contribution-based ESA which will terminate after twelve months.
Income-based ESA will continue beyond the twelve month period, but you will need to satisfy a means test in order to continue to receive the allowance. This will depend on your household circumstances and will take into account such items as the total amount of income and capital/savings.
This will not apply to ESA claimants who are placed in the support group. These claimants will continue to receive contribution-based ESA, as long as they continue to meet the conditions of entitlement to remain in the SG.
Nothing on this board constitutes legal advice - always consult a professional about specific problems