Reversible cross-linking is an effective strategy to specifically tailor the mechanical properties of polymeric materials that can be found in a variety of biological as well as man-made materials. Using a simple model in this paper the influence of weak, reversible cross-links on the mechanical properties of aligned fiber bundles is investigated. Special emphasis in this analysis is put on the strength of the investigated structures. Using Monte Carlo methods two topologies of cross-links exceeding the strength of the covalent backbone are studied. Most surprisingly only two cross-links are sufficient to break the backbone of a multi chain system, resulting in a reduced strength of the material. The found effect crucially depends on the ratio of inter- to intra-chain cross-links and, thus, on the grafting density that determines this ratio.