Have you seen this written down, Deyss, or have you heard it spoken?
I am asking because if you have heard it, it could possibly have been '... the last effin' box ...' with the 't' of 'last' running into 'effin''- 'effin'' being a politer way of saying 'fucking'.
On the other hand, a tiffin box can mean a lunch box:
http://en.wikipedia.org/wiki/Tiffin
Does either of those possibilities fit your context?