The relationship between the parent company and its subsidiaries is that they are independent companies, and if there is a relationship, there is only joint and several liability. AIA doesn't depend on AIG, so it won't be affected too much, at least there is no problem in continuing to operate.
AIG can transfer the shares of AIA at most, which means that a larger consortium may acquire AIA, which has no impact on AIA as a whole.
In addition, insurance companies are not allowed to close down. Don't worry, all your insurance will not be affected. I am an agent of AIA and a customer of AIA.