Just a layman way of saying it is outside the manifold. In plain words, a hole, or a throat, appears on the space-time fabric as with a Flamm surface, which is not contractile and has no center.
Thanks for your explanations, indeed Schzartchild used r as a simple parameter which has been wrongly understood to be a radius but in his mind it was never the case at all. According to Weyl, when M grows bigger than 2.5 solar masses then the proper mass is inverted. Weyl wrote his article in 1917 but was translated only 90 years or so later so Oppenheimer and Wheeler had not read it when they invented the singularity-based BH model many years later. According to Schwarschild, if r becomes smaller than Rs then the ds squared becomes negative, hence we are outside the hypersurface. Tolman and Oppenheimer only forgot about the preriquisite condition r > Rs (that’s what I mentionned as "corrupted"). IMO only a mathematical singularity can make sense, believing in a physical one is like believing flat oceans could have no borders. So yes, Kruskal and Oppenheimer theorized time and space directions inversion to allow for time to flow endlessly into the singularity but, as for the flat Earth borders, it seems far from substantiated.