I don't think you can call dimensions, or their related coordinates (or systems) a "fabric", in any way other than informally. To posit a "tear" in a "fabric" is really the linguistic equivalent to "drilling a hole in the AEther."
I think chroot was probably pointing out that modern (accepted) physics does away with the notion of an ether, or substrate to reality. The existence of dimensions doesn't imply that they form an "interwoven fabric". That's a great way to describe spacetime without math, but it's not physical.
It's hard if not impossible to imagine a play without a backdrop, but really that's what the universe seems to be. Unless you posit Branes, or other purely theoretical constructs, 4-dimensions don't describe a fabric that can be "torn". Beyond speculation, there is no reason to believe that a singularity represents a "tear", but a departure from the norm. In theory, that BH may evaporate through HR, and what would be left is presumably NOT a "tear" or a "hole", just radiation.
@IttyBittyBit: Oh please, are you going to tell us about technological singularities next? We're talking about spacetime in the relativity forum, and you seem bright enough to grasp "context". Don't blow smoke up all of our ****es, and don't extend this anymore than needs be with prattle about basics we all learned in grade-school.