The pronoun has nothing to do with it. Lists do not work that way in the first place. In your example, you should only have one conjunction.

For example:

Claims are not liable to insurers, investors, S Corporation, or its owners.

First of all, your first example is incorrect as a list can only have one conjunction.

To answer your question, 'or' is the correct conjunction. 'And' is not applicable because this list is about something that does not happen, and 'nor' is only used after 'neither' as in:

Neither John nor Bob wanted to go to the supermarket.

Therefore, your sentence should look like this:

Claims are not liable to insurers, investors, S Corporation, or its owners.

The pronoun has nothing to do with it. Lists do not work that way in the first place. In your example, you should only have one conjunction.

For example:
Claims are not liable to insurers, investors, S Corporation, or its owners.Example:

The pronoun has nothing to do with it. Lists do not work that way in the first place. In your example, you should only have one conjunction.

For example:

Claims are not liable to insurers, investors, S Corporation, or its owners.