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Presumably you mean when it runs out of power to the point that it is no longer capable of transmitting at all. If it is, for example, Voyager, then it will continue to drift out into deep space for probably longer than the human species will exist. It might eventually fall into the gravity well of a black hole somewhere, but space is unfathomably vast, so it is probably just going to drift forever.

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14y ago

What else can I help you with?