POP3 is a protocol by which a client (such as Deskpro) connects to a server (your mail server) to download emails. POP3 itself is an extremely simple protocol. The only thing it allows is essentially: List messages, download messages, and then delete messages.
It's important to note that with POP3, there is no concept of folders, there is no concept of a message being read or unread, there is no "trash" that deleted messages go into, etc. Only those three actions described above are supported.
So when you configure a POP3 account in Deskpro, there are no read options to choose from because POP3 just has no features. The only way Deskpro can process POP3 is to download them, then delete them.
When delete doesn't delete...
Some providers, such as Gmail, add special handling for POP3. For example, here's Gmail settings for POP3:
As you see here, Gmail adds special magic over the POP3 protocol, giving you an option about from when to make messages available, and also what to do when messages are deleted from a POP3. For example, many people choose to archive messages. This means that when a client (such as Deskpro) deletes a message, Gmail archives the message instead.
But the point to remember is that this is behaviour that Deskpro has no control over. POP3 does not allow any kind of customisation like this, it's just an extra, non-standard feature Gmail adds.
Gmail was used here as an example, but other providers may offer similar features.