Hearth
The hearth — the household fireplace from which a coal could be carried — appears explicitly in only one of the verses gathered under this umbrella. Two related references concern household fire, but in UPDV they speak instead of a brazier or omit the hearth altogether.
A coal from the hearth
The hearth's everyday function is to keep a live fire from which a person could lift a glowing fragment with a potsherd. Isaiah's image of total destruction works against exactly that ordinary use: "And he will break it as a potter's vessel is broken, breaking it in pieces without sparing; so that there will not be found among its pieces a sherd with which to take fire from the hearth, or to dip up water out of the cistern" (Isa 30:14). The shattering is so thorough that even the smallest serviceable fragment — large enough to scoop up an ember from the hearth — is left.
Related fires named differently
Two related references treat household fire under different terms in UPDV. Abraham's hospitality at the tent involves bread-making — "And Abraham hurried into the tent to Sarah, and said, Quickly prepare three seahs of fine meal, knead it, and make cakes" (Gen 18:6) — but UPDV's wording does not name a hearth. Jehoiakim's fire in the winter-house, on which he burns Jeremiah's scroll, is identified by a different vessel: "Now the king was sitting in the winter-house in the ninth month: and [there was a fire in] the brazier burning before him. And it came to pass, when Jehudi had read three or four leaves, that [the king] cut it with the penknife, and cast it into the fire that was in the brazier, until all the roll was consumed in the fire that was in the brazier" (Jer 36:22-23). The fire is real and central to the scene, but UPDV calls its container a brazier, not a hearth.