“Weakness of character is the only defect which cannot be amended.” -Francois de La Rochefoucauld
So, you’d like to ruin the fabric of your space, would you? Similar to tying a knot in it, stitching it up with some poorly-run shenanigans, running a two-dimensional membrane through it (like a hole in a sponge), etc., it’s possible to put a topological defect in the fabric of space itself. This isn’t just a mathematical possibility, but a physical one: if you break a symmetry in just the right way, monopoles, strings, domain walls, or textures could be produced on a cosmic scale.
These could show up in a variety of ways, from abundant new, massive particles to a network of large-scale structure defects in space to a particular set of fluctuations in the cosmic microwave background. Yet when it comes time to put up or shut up, the Universe offers no positive evidence of any of these defects. Save for one, that is: back in 1982, there was an observation of one (and only one) event consistent with a magnetic monopole. 35 years later, we still don’t know what it was.