Variational and diffusion Monte Carlo (VMC and DMC) calculations are presented for anionic electrolytes solvated in (4)He. The electrolytes have the general structure X(-)(He)(N), with X=F, Cl, Br and I, and N varying up to 40 (41 for I(-)). The overall interaction potential is obtained from accurate ab initio data for the two-body components and then using the sum-of-potentials approximation. Our computational scheme is a robust procedure, giving us accurate trial wavefunctions that can be used to perform high-quality DMC calculations. The results indicate very marked delocalization and permanence of the liquid-like quantum features of the solvent adatoms surrounding the anionic impurities. This finding stands in contrast to the more structured, solid-like behavior of the quantum solutions with alkali metal cations embedded in He nanodroplets. While other negatively charged species such as H(-) have shown an overall repulsive interaction with He, the present calculations clearly indicate that the halogen anions remain solvated within liquid-like solvent "bubbles" of species-dependent size.