A fireplace where the firewood had run short and the flames were already beginning to wane.

Literal

Firewood [subject-が] be-insufficient-[classical-negative-stem-ず], already fire-strength [subject-が] wane-begun fireplace.

A literary 体言止め (noun-ending) sentence with a complex pre-nominal modifier. Two features of written/literary register: (1) 足りず uses the classical negative stem-form ~ず ('not X-ing'), which links clauses without a te-form — a more compact, formal alternative to 足りなくて; and (2) the whole relative clause sits before 暖炉 ('fireplace') without any relative pronoun, typical of Japanese. 火勢 ('fire strength, intensity of the flames') is a formal compound. 衰え始める 'begin to wane' stacks 衰える + 始める.