What happens to his account and portfolio in such an event?
Is it possible that a third party can start using the account?
If by account you mean his bitcointalk account, it was his and his alone and cannot be used by anyone even after his demise. The account represents his character, trust and judgement and cannot to be handed over to a different user, that's why an account is normally tagged whenever it changes hands. Though in the memorial thread someone suggested that his daughter should use it, don't know if the forum is going to make an exception.
Concerning his portfolio, as long as someone he trusted with the seed phrase still has it, the funds can be spent.