The importance of tissue remodelling is widely accepted, but the mechanism by which the remodelling process occurs remains poorly understood. At the tissue scale, the concept of tensional homeostasis, in which there exists a target stress for a cell and remodelling functions to move the cell stress towards that target, is an important foundation for much theoretical work. We present here a theoretical model of a cell in parallel with a network to study what factors of the remodelling process help the cell move towards mechanical stability. The cell-network system was deformed and kept at constant stress. Remodelling was modelled by simulating strain-dependent degradation of collagen fibres and four different cases of collagen addition. The model did not lead to complete tensional homeostasis in the range of conditions studied, but it showed how different expressions for deposition and removal of collagen in a fibre network can interact to modulate the cell's ability to shield itself from an imposed stress by remodelling the surroundings. This study also showed how delicate the balance between deposition and removal rates is and how sensitive the remodelling process is to small changes in the remodelling rules.