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Usually such sets had a capacitor that coupled the ground of the aux input jack to the set's internal ground. Usually 0.1uF, sized to pass low frequencies reasonably well in a high impedance circuit, but to limit shocking current if a user gets between the aux jack ground and an external grounded item (and the set's internal ground happens to be connected to the hot side of the powerline).
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Yeah, that inspires a lot of confidence, doesn't it? ;-)