In various biological scenarios, active cellular tissues initially adhere to the fibrous extracellular matrix (ECM) and then penetrate to become (partially) engulfed inside it. This occurs in a variety of processes such as branching morphogenesis, angiogenesis, embryo implantation, hair follicle development, and cancer invasion. In principle, such engulfment could result from the elastic deformation of the ECM caused by active tensions within the cellular tissue, akin to elastocapillarity, or from the chemical degradation of the ECM, or a combination of both processes. While the tissue shape may appear similar, the ECM’s mechanical state, and thus the mechanosensitive mechanisms driving invasion, differ substantially. This work seeks to clarify the fundamental dynamics that produce a variety of similar yet distinct phenomena resulting from the convergence of two distinct behaviours: indentation and degradation. More precisely, we examine these scenarios by a continuum mathematical model for an active fluid, representing a cellular tissue, over a hyperelastic solid matrix, undergoing localized erosion at the fluid-solid interface. This surface degradation requires particle removal from the solid interface, implying a non-material moving boundary and a time-dependent material manifold. The numerical method developed to address this relies on non-conforming meshes. Specifically, the moving interface problem resulting from the solid-fluid interaction with localized interfacial degradation is studied through a Nitsche-Onsager variational formulation of the problem. The findings of this study suggest that, in the analysis of complex mechanobiological processes, the simultaneous presence of active cell tractions, capillary forces, and degradation processes, if not properly distinguished, can obscure their individual contributions. This interaction dramatically modifies the mechanical state of the ECM, and the resulting stress distribution within the solid matrix may vary depending on which component prevails, thereby shaping the tissue’s chemo-mechanical behaviour.