The last Block you mine before the shears break doesn't drop what it should or what you expect the drop to be. It depends on what Block you mine, not all Blocks which are mineable by shears are affected.

To Reproduce this Issue, give yourself Shears with 1 Durability remaining:

/give @s minecraft:shears{Damage:237} 1

Then mine any type of Leaves and they won't drop what they're supposed to: a Leave Block. What's weird is that sometimes you get 2 sticks or a sapling to drop. It's almost as if you mined it with your Hand.

I also tried Low and Tall Grass. Low Grass doesn't drop itself and Tall Grass drops 2 grass as expected.

Cobweb does drop 1 String instead of a cobweb like you would expect.