This response assumes linear elastic analysis. If you're doing a post-failure plactic analysis then please disregard this post
The idea behind bucking failure is that the structure becomes unstable if a load higher than Pcr is applied.
If the structure is unstable, then by definition the post-buckling deflection is undefined.
Picture a long column, like a 20' long piece of 1" pipe. For a non-eccentric load, below the critical buckling load, lateral deflection of the pipe is essentially zero. Once the pipe buckles, the deflection keeps increasing until the load is on the floor.
-Dan