A design intern's role can vary from running minor errands and making tea to tweaking designs but on rare occassions, a design intern is given the opportunity to design; the opportunity to create something from nothing; to research and generate ideas independently for a genuine paying client. When this happens, it is the perfect opportunity to impress, not just this agency but others too. This work will lead to an actual product so you want to keep the evidence. You want proof that you did it and after a good full week working on it, you want to take it home.
Confidentiality agreements state that you will infact be sued and left penniless, having to busk on the Southbank as a caricature artist because no design agency will have you, should you dare tell anyone about their work in progress. Despite this threat, every intern will spend their last day e-mailing main files, linked images and psds to their own e-mail address hoping that no one will notice.
Stealing work is important. A placement is more than just a name on your cv, you want to be able to say; "I did this". You need to be able to show what you can do; your work. Sure I won't show anyone but I want it anyway. After all it is mine.