The Inbox is where one recieves communications and items in Force Collection. It is divided into three tabs: Expires Soon, No expiration, from Players. There is no known maximum allowed number of items.
The "No Expiration" tab is where Cards you receive from Corellian Gambits, Events or from Trades that were canceled. As the name suspects, those cards will never expire and can be taken at any time you want.
From Players Edit
The "From Players" tab is where cards from Trades and gifts land. They also have no Expiration.