Something's really, really off here.
If they were using POP, all storage long term should be local (as in on their machine) only. Every message that gets downloaded is purged somewhere between immediately afterward or a short time afterward UNLESS someone went in and tweaked POP settings to prevent this. The Sent folder should be local.
You have never said who the email service provider is, but it's a virtual certainty that they have a webmail interface. You really need to log in to this account via webmail to see "what's what" on the server side as the provider is seeing it. It's the only way (or only easy way) you are going to be able to accurately assess what the storage situation actually is.