In this paper, we study a diffusive prey-predator model with Beddington-DeAngelis functional response when the intraspecific crowding effect for the prey population disappears in some subdomain Ω0 of their whole habitat. We are concerned about the global dynamics of the system and discuss it based on two coefficients: the growth rate of prey λ and that of predator μ. In particular, the results show that, with the degeneracy of prey population's intraspecific crowding effect in the subdomain Ω0, the density of prey may tend to infinity in Ω0. On the other hand, the unboundedness of prey means that the solutions of the system lose compactness which may bring difficulty to investigate the long-time behavior of the solutions. Finally, some numerical simulations are presented to support and strengthen our theoretical analysis.