Peer-to-peer (P2P) communication in networks for file distribution and other applications is a powerful multiplier of network utility, due to its ability to exploit parallelism in a distributed way. As new variations are engineered, to provide less impact on service providers and to provide better quality of service, it is important to have a theoretical underpinning, to weigh the effectiveness of various methods for enhancing the service. This paper focuses on the stationary portion of file download in an unstructured P2P network, which typically follows for many hours after a flash crowd initiation. The contribution of the paper is to identify how much help is needed from the seeds, either fixed seeds or peers dwelling in the system after obtaining the complete file, to stabilize the system. It is shown that dominant cause for instability is the missing piece syndrome, whereby one piece becomes very rare in the network. It is shown that very little dwell time is necessary - even if there is very little help from a fixed seed, peers need to dwell on average no longer than it takes to upload one additional piece, after they have obtained a complete collection.