A metastable complex defect in S-doped silicon has been studied with zero-field optically-detected magnetic-resonance (ODMR) spectroscopy. The defect shows two characteristic photoluminescence (PL) spectra S(A) and S(B), corresponding to two different geometric configurations 1 and 2. The PL spectra in both cases originate from excited-state triplet bound excitons in the neutral charge state of the defect. Previous X-band ODMR studies for S(A) and S(B) show broad spectra with unresolved hyperfine interaction. In zero-field ODMR the linewidth is reduced to about 50 MHz for S(A) (100 MHz for S(B)), and the second-order hyperfine structure of an I = 3/2 nucleus is resolved, partly with the help of a double-resonance technique. The zero-field splitting parameters of the triplet states (i.e., the principal D-tensor components) are determined as D(xx) = -2905, D(yy) = -705, and D(zz) = 3610 MHz for S(A), and D(xx) = -1295, D(yy) = -180, and D(zz) = 1475 MHz for S(B). The hyperfine splitting is determined as A = 175 MHz for both S(A) and S(B), whereas the quadrupole constant P(z'z') has a value 10-20 MHz for S(A) and a substantially larger value, 30-40 MHz for S(B). The I = 3/2 nucleus at the core of the defect is tentatively identified as Cu. The conclusion about the different quadrupole interaction for S(A) and S(B) from these data agrees with previous ODMR X-band data in a magnetic field, which also show a different configuration (of the Cu atom) in the excited triplet states of S(A) and S(B). It is tentatively concluded from these data that the metastability of this defect is connected to a change of the site of the Cu atom with respect to its surroundings in the silicon lattice.