New isotopic studies of 142Nd, the daughter product of the short-lived and now extinct isotope 146Sm, have revealed that the accessible part of the silicate Earth (e.g., upper mantle and crust) is more radiogenic in 142Nd/144Nd than that of chondritic meteorites. The positive 142Nd anomaly of the Earth's mantle implies that the Sm/Nd ratio of the mantle was fractionated early in Earth's history and that the complementary low 142Nd reservoir has remained isolated from the mantle since its formation. This has led to the suggestion that an early enriched reservoir, formed within Earth's first hundred million years (the Hadean), resides permanently in the deep interior of the Earth. One hypothesis for a permanently isolated reservoir is that there may be an Fe-rich, and hence intrinsically dense, chemical boundary layer at the core-mantle boundary. The protoliths of this chemical boundary layer could have originated at upper mantle pressures during extreme fractional crystallization of a global magma ocean during the Hadean but testing this hypothesis is difficult because samples of this early enriched reservoir do not exist. This hypothesis, however, is potentially refutable. Here, we investigate a post-Archean magnetite-sulfide magma formed by extreme magmatic differentiation to test whether residual Fe-rich liquids of any kind have the necessary trace-element signatures to satisfy certain global geochemical imbalances. The magnetite-sulfide magma is found to have high Pb contents (and low U/Pb ratios), high Re/Os ratios, and anti-correlated Sm/Nd and Lu/Hf fractionations. Permanent segregation of such a magma would (1) provide a means of early Pb sequestration, resulting in the high U/Pb ratio of the bulk silicate Earth, (2) be a source of radiogenic 187Os in the source regions of plumes, and (3) provide an explanation for decoupled Hf and Nd isotopic evolution in the early Archean, which is not easily produced by silicate fractionation. However, the magnetite-sulfide magma is not highly enriched in K, and thus, at face value, this magma analog would not serve as a repository for all of the heat producing elements. Nevertheless, other Fe-O-S liquids reported elsewhere are enriched in apatite, which carries high concentrations of K, U and Th. Given some promising geochemical fractionations of the Fe-rich liquids investigated here, the notion of a Hadean Fe-rich residual liquid deserves continued consideration from additional experimental or analog studies.