When a knife is at extremely low durability (likely only one use from breaking, with the description "it's about to break") then it seems to delete whatever you try to chop using it, but the knife itself never properly breaks. 

For example, when trying to cut 5 alicorns, all 5 alicorns vanish along with the knife. However, the knife doesn't provide a message that it has broken, nor does it drop any scraps. Upon relogging, the knife re-appears but the food does not. Meanwhile, a knife that isn't nearly broken still functions as intended.