It will initially be considered the asymptotic behavior of the solution of a mean-field system of Backward Stochastic Differential Equations with Jumps (BSDEs), as the multitude of the system equations grows to infinity, to independent and identically distributed (IID) solutions of McKean–Vlasov BSDEs. This property is known in the literature as backward propagation of chaos. Afterwards, it will be provided the suitable framework for the stability of the aforementioned property to hold. In other words, assuming a sequence of mean-field systems of BSDEs which propagate chaos, then their solutions, as the multitude of the system equations grows to infinity, approximates an IID sequence of solutions of the limiting McKean–Vlasov BSDE. The generality of the framework allows to incorporate either discrete-time or continuous-time approximating mean-field BSDE systems.