We consider a time-fractional subdiffusion equation with a Caputo derivative in time, a general second-order elliptic spatial operator, and a right-hand side that is non-smooth in time. The presence of the latter may lead to locking problems in our time stepping procedure recently introduced in [J. Comp. Appl. Math., 427(115122), 2023]  and [Appl. Math. Lett., 123: Paper No. 107515, 8, 2022]. Hence, a generalized version of the residual barrier is proposed here to rectify the issue. We also consider related alternatives to this generalized algorithm, and, furthermore, show that this new residual barrier may be useful in the case of a negative reaction coefficient.