If a bitcoin wallet service provider terminates a users account, what happens to the funds?
This is why people say "Not your keys, not your bitcoin. Your keys, your bitcoin". The online marketplace owner owns the private key of the address that your friend used to fund his account. The owner of the marketplace can always say he lost the private key of your friends' account, but if he wants, he can prove ownership by signing a message with the private key (he has nothing to gain though).

Your friend should provide a new address to the owner of this marketplace and ask him to send the bitcoin that he had to that address, otherwise, yes, he is probably stealing.