Interesting Secret Santa problem

Consider a game of secret Santa, where people take turns opening presents. On your turn you may either open one or steal a previous person's present, who may also opt to steal or open, but may not steal an object that has been stolen this turn. Suppose n people, and some additional non-standard rules. In particular, to prevent bullying a single person, an individual may not be stolen from more than i times, and so nobody feels bad about putting a less popular present in, no object can be stolen more than j times. What would you use to model this, and are there properties of i, j, and n for which we may end up with a scenario where a person cannot steal (who is not the final person in a round)?

To be clear, by final person in a round, I mean that in an individual round, say the kth round, the kth person is the final person.