If a bitcoin wallet service provider terminates a users account, what happens to the funds? A friend of mine has/had a bitcoin wallet service provided by an online marketplace. Sounds like he had some kind of disagreement with the site administrators and they terminated his account. At that time, he still had some BTC in the wallet. Not a lot (about $50.00 USD or so), but still. 

Is there any way to recover the funds, or are we all at the mercy of our wallet service providers in that respect?  

Seeing as all transactions are recorded in the ledger, I figured perhaps there's some way to claim/prove/declare ownership. It seems pretty thin, but surely there's some kind of safeguard in place, otherwise wallet service providers could exploit that trust and just terminate all their customers accounts and take all their funds with impunity at any moment. Right?
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.