We study the formation of large hyper-fragments in relativistic heavy-ion collisions within two transport models, DCM and UrQMD. Our goal is to explore a new mechanism for the formation of strange nuclear systems via capture of hyperons by relatively cold spectator matter produced in semi-peripheral collisions. We investigate basic characteristics of the produced hyper-spectators and evaluate the production probabilities of multi-strange systems. Advantages of the proposed mechanisms over an alternative coalescence mechanism are analysed. We also discuss how such systems can be detected taking into account the background of free hyperons. This investigation is important for the development of new experimental methods for producing hyper-nuclei in peripheral relativistic nucleus-nucleus collisions, which are now underway at GSI and are planned for the future FAIR and NICA facilities.