The problem of computing approximate stationary points of non-convex landscapes has received extensive scrutiny in optimization and machine learning literature. It was established quite recently that finding approximate stationary points for non-convex, smooth, bounded functions defined in unrestricted domains is complete for the class PLS [Hollender and Zampetakis, COLT 2023]. Nevertheless, the main obstacle in non-convex optimization is the existence of saddle points, i.e., stationary points of negative curvature which can outnumber the number of local minima. In this paper, we focus on the problem of finding approximate stationary points that are \textit{not strict saddle}, i.e., \textit{second-order} stationary points. We show that the aforementioned problem is also complete for the class PLS, answering an open question asked in [Hollender and Zampetakis, COLT 2023]. Our results imply that, unless PLS = NP, finding approximate second-order stationary points in unrestricted domains is easier than in (restricted) linear constrained domains, which is known to be NP-hard [Nouiehed et al, 2018]. This comes in contrast with the result in [Hollender and Zampetakis, COLT 2023] and [Fearnley et al, JACM 2022] from which is surprisingly implied that unless PLS = CLS, finding approximate stationary points in unrestricted domains is harder than in (restricted) linear constrained domains.