Insurance for director

Hi

Can anyone please tell that if a company takes up any of the following insurance policies for his director and pays for it also, whether any tabalility would fall on the director at any point of time. Following are the options for the policies that can be taken by the comapny :-

• Individual Policy for Director
• Group Policy for eberyone including the director
• Keyman Policy 

Would appreciate the reply.

Thanx in advance.

Saurabh