This is a question that takes us back to earlier discussions of how proteins work. As you may recall, proteins (like egg proteins, for example), are extremely long molecules made up of chains of amino acids. In their natural state they occur loosely coiled, or “folded”. Yet by applying gentle heat we can coax their bonds to release, at which point they unfold into languid chains with free bonding sites on them. As these chains move about in the heat those exposed sites start bonding to other protein molecules, creating a lattice which (in a process not entirely dissimilar from a starch gel or gluten network) traps and holds water molecules. It’s called coagulation, and it’s how liquid eggs turn solid as they cook.
There is however a limit to the benefits of heat on proteins. Too much of it and the proteins start to bond too tightly to one another. The lattice tightens, squeezing water out like a fist tightening around a sponge. It’s this process that turns scrambled eggs to rubber when they’re left too long in the pan.
In the case of a flourless chocolate cake, curdling turns the cake into a hard, chalky chocolate puck floating in a small puddle of water. Most people, however, don’t really notice it. They look in the pan and think that either the liquid is separated butter or seepage from a pinhole in their pan liner. In fact what happened is they missed out on the dense chocolate custard their cake was supposed to be. The results are still edible, though a mere shell of what could have been.