We study the rate-independent decohesion process for a chain linked to a substrate through a series of breakable elements with a softening mechanism. Such an assumption describes the realistic case when connecting links can undergo softening transitions before breaking. For instance, this is a diffuse mechanism observed both in fracture of soft materials and biological adhesion. The analysis of this model is developed in the framework of equilibrium statistical mechanics. In order to describe mechanically induced detachment of the chain from the substrate both in the cases of hard devices (prescribed extension) or soft devices (applied force), we consider both Helmholtz and Gibbs ensembles. In any case, the model can be exactly solved and is characterized by a phase transition at a given critical temperature, corresponding to the complete detachment of the chain even without mechanical actions. Interestingly, according to the 'size' of the softened region, we observe two different regimes. In one case (fragile regime) during the decohesion the measure of the softened region is negligible, whereas in the other case (ductile regime) we obtain a finite measure of the softened region that is constant, giving a temperature dependent analytic measure of the process zone.