Keilim 4:1-2

Keilim 4:1

If the shard of a broken earthenware vessel cannot stand because of its handle, or it had a point on which it cannot stand, it is not susceptible to ritual impurity. If the handle or point is broken off, it remain insusceptible, though Rabbi Yehuda declares it susceptible. If a jar lost its bottom but the sides can still function as a receptacle, or if it split in half into two trough-like pieces, Rabbi Yehuda rules it insusceptible to ritual impurity, while the Sages rule it susceptible.

Keilim 4:2

If a jar cracks so that it cannot be carried around holding half a kav of dried figs (one meal’s worth) without breaking, it is not susceptible to ritual impurity. If a shard is cracked and can’t hold liquid, though it can hold food, it is not susceptible to ritual impurity. This is because there is a concept of remnants of vessels but there’s no concept of remnants of remnants.