You are not 100% correct here:
1- Health Insurance or Mediclaim - Only Sum Insured exhausted. You can't claim against that policy until renewal. On renewal - you can renew as normal.
2- Critical Illness - If Sum Insured exhausted the policy stands automatically terminated. You can't renew. But you can buy a new policy.
3- Personal Accident - If Sum Insured exhausted the policy stands automatically terminated. You can't renew. But you can buy a new policy.