Rings whose non-invertible elements are weakly nil-clean

In regard to our recent studies of rings with (strongly, weakly) nil-clean-like properties, we explore in-depth both the structural and characterization properties of those rings whose elements that are not units are weakly nil-clean. Group rings of this sort are considered and described as well. This somewhat supplies our recent results of this branch when the units are weakly nil-clean published in Punjab University Journal of Mathematics (2024).