The problem of interference management is considered in the context of a linear interference network that is subject to long term channel fluctuations due to shadow fading. The fading model used is one where each link in the network is subject independently to erasure with probability p. It is assumed that each receiver in the network is interested in one unique message, which is made available at M transmitters. Optimal schemes from a Degrees of Freedom (DoF) viewpoint are analyzed for the setting of no erasures, and new schemes are proposed with better average DoF performance at higher probabilities of erasure. Additionally, for M=1, the average per user DoF is characterized for every value of p, and optimal message assignments are identified. For M>1, it is first established that there is no strategy for assigning messages to transmitters in networks that is optimal for all values of p. The optimal cooperative zero-forcing scheme for M=2 is then identified, and shown to be information-theoretically optimal when the size of the largest subnetwork that contains no erased links is at most five.