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We consider a rate-independent system with nonconvex energy underdiscontinuous external loading. The underlying space is finite dimensional andthe loads are functions in $BV([0,T];\mathbb{R}^d)$. We investigate thestability of various solution concepts w.r.t. a sequence of loads convergingweakly$*$ in $BV([0,T];\mathbb{R}^d)$ with a particular emphasis on theso-called normalized, $\mathfrak{p}$-parametrized balanced viscosity solutions.By means of two counterexamples, it is shown that common solution concepts arenot stable w.r.t. weak$*$ convergence of loads in the sense that a limit of asequence of solutions associated with these loads need not be a solutioncorresponding to the load in the limit. We moreover introduce a new solutionconcept, which is stable in this sense, but our examples show that this conceptnecessarily allows "solutions" that are physically meaningless.

On a Lack of Stability of Parametrized BV Solutions to Rate-Independent Systems with Non-Convex Energies and Discontinuous Loads