A source communicates with a remote destination via a number of distributed relays. Communication from source to relays takes place over a (discrete or Gaussian) broadcast channel, while the relays are connected to the receiver via orthogonal finite-capacity links. Unknowns to the source and relays, link failures may occur between any subset of relays and the destination in a nonergodic fashion. Upper and lower bounds are derived on average achievable rates with respect to the prior distribution of the link failures, assuming the relays to be oblivious to the source codebook. The lower bounds are obtained by proposing strategies that combine the broadcast coding approach, previously investigated for quasi-static fading channels, and different robust distributed compression techniques. Numerical results show that lower and upper bounds are quite close over most operating regimes, and provide insight into optimal transmission design choices for the scenario at hand. Extension to the case of nonoblivious relays is also discussed.