The black plastic-like substance molded around the tang of our daily driver kitchen knife crumbled away near the blade and eventually reached the point my thumb couldn’t stand it any more. Given the good results of the JB Weld coating on the cheese slicer (which is still going strong after four years), I chipped away the loose fragments on all sides, wire-brushed the crater with alcohol, and filled it with epoxy:

The Kapton tape bridges the solid part of the handle with the metal just behind the blade, holding the epoxy in more-or-less the right shape while it cured overnight. The other side looks much the same, which is why I couldn’t just let it sit out.
A few minutes with a file and wire wheel knocked back the high spots and left it looking much better than before, if a bit scuffed:

The tang inside the molded shell is kinda-sorta cruciform, with an exposed rib along both sides. I think the plastic shrank around the tang in that gap between the ribs and the blade, where its lack of flexibility caused the cracks.
Neither a beautiful restoration nor a permanent fix, but it ought to last for a while. Similar cracks at the hilt end of the handle suggest more repairs lie in its future.