  New physics beyond General Relativity impacts black-hole spacetimes. The
effects of new physics can be investigated in a largely theory-agnostic way by
following the principled-parameterized approach. In this approach, a classical
black-hole metric is upgraded by following a set of principles, such as
regularity, i.e., the absence of curvature singularities. We expect these
principles to hold in many theories beyond General Relativity. In the present
paper, we implement this approach for time-dependent spacetimes describing
gravitational collapse. We find that the Vaidya spacetime becomes regular
through the same modification of the spacetime metric as stationary black-hole
spacetimes [1-3]. We investigate null geodesics and find indications that the
modification is even sufficient to render null geodesics future complete.
Finally, we find that the modification of the spacetime structure results in
violations of the null energy condition in a finite region inside the apparent
horizon of the black hole that forms. Null geodesics are attracted to the
boundary of this region, such that the new-physics effects are shielded from
asymptotic observers. An exception occurs, if the classical spacetime has a
naked singularity. Then, the upgraded spacetime is singularity-free and null
geodesics from the regular core can escape towards asymptotic observers.
