The mediclaim/group mediclaim policy arranged by majority of the employer ends on the last day of the employment. The employment may end due to resignation, termination, retirement etc.
It is better to obtain individual mediclaim policy also for self + family +dependant parents even if the company provides mediclaim/group mediclaim policy. Majority of the policies if renewed well in time provide insurance cover up to the age of 80 years. If the policy is renewed a month in advance the medical tests are not necessary. The premium is nominal and affordable and is entitled for tax relief under section 80(D). One should compare the policies and should choose the insurer and plan carefully depending upon the inclusion and exclusion criteria. If you change the insurer some of the companies consider policy issued by them as a new policy and impose conditions that some of the diseases shall not be covered for first 2-3 years.
Some of the banks have tie up with General Insurance companies e.g. Canara Bank with United India Insurance Company Ltd (both of these are public sector undertakings) and a/c holders of the bank can avail the policy at lower premium.