||The vast majority of soft and biological materials, gels, and tissues are made from micrometer-size slender structures such as biofilaments and colloidal and molecular chains, which are believed to crucially control their mechanics. These constituents show intriguing extreme mechanics, mechanical instabilities, and plasticity, which, besides attracting significant theoretical attention, have not been studied experimentally and as such remain poorly understood. Here we investigate, by experiments, simulations, and theory, the mechanical instabilities of a slender self-assembled colloidal structure, observing a form of stochastic buckling where thermal fluctuations and associated entropic force effects are amplified in the vicinity of a buckling instability. We fully characterize how the persistence length and plasticity control the stochastic buckling transition, leading to intriguing higher-order buckling modes. These results elucidate the interplay of geometrical, thermal, and plastic interactions in the nonlinear mechanics of thermal self-assembled structures, crucial to the mechanical response and function of fiber-based soft and biological materials, as well as the rational design of micro- and nanoscale architectures.