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We study a chemically active binary mixture undergoing phase separation and show that under nonequilibrium conditions, stable liquid spherical shells can form via a spinodal instability in the droplet center. A single liquid shell tends to grow until it undergoes a shape instability beyond a critical size. In an active emulsion, many stable and stationary liquid shells can coexist. We discuss conditions under which liquid shells are stable and dominant as compared to regimes where droplets undergo shape instabilities and divide.