We consider the archetypal frustrated antiferromagnet SrCr(9p)Ga(12-9p)O₁₉ in its well-known spin-liquid state, and demonstrate that a Cr(3+) spin S=3/2 ion in direct proximity to a pair of vacancies (in disordered p<1 samples) is cloaked by a spatially extended spin texture that encodes the correlations of the parent spin liquid. In this spin-liquid regime, our analytic theory predicts that the combined object has a magnetic response identical to a classical spin of length S/2=3/4, which dominates over the small intrinsic susceptibility of the pure system. This fractional-spin texture leaves an unmistakable imprint on the measured ⁷¹Ga nuclear magnetic resonance line shapes, which we compute using Monte Carlo simulations and compare with experimental data.