Studying the small-signal stability for multi-parallel voltage source converter (VSC)-based renewable energy plants (REPs) during the fault steady-state of low-voltage ride-through (LVRT) in weak grid is significant for designing a stabilized controller to ensure and improve success of LVRT. Different from the independent grid-connected system and symmetric condition, in the asymmetrical fault steady-state, there are more complicated dynamic interactions between the positive-sequence (PS) and negative-sequence (NS) systems as well as between the REPs in multi-fed grid-connected system. This study unveils the dynamic coupling mechanism between REPs by deduced small-signal model during asymmetric LVRT, which provides a solid foundation for designing the novel stabilized controllers. The influence of this dynamic coupling effect between REPs on the system's small-signal stability in the asymmetrical fault steady-state is analyzed. It's shown that the dynamic coupling between REPs will be aggravated by the deteriorating asymmetrical fault, and it will cause the existing stabilized controller's performance decreasing or even invalid. Combining with small-signal stability analysis, the asymmetric fault degree's influencing mechanism on small-signal stability of multi-fed grid-connected system is revealed from the perspective of self-damping and mutual damping. Finally, simulations and experiments are carried out to validate analysis results.