Short answer: (not tied to satellite) it would just fall down.
Tied to satellite: it would follow the satellites orbit of the earth. The cord would be whipped up from the earth and be a continuous loop of orbit, like a child running holding up a string on a stick. The string would follow the child’s path and direction as long as the child is running.
But if you mean that the cord is also tied to the earth and a satellite at the same time, then the answer is unknown. There’s actually a concept called “Space Elevator” which is a theoretical structure that could extend from the surface of the Earth into space. The idea is to have a cable or ribbon stretching from the ground to a counterweight or space station in geostationary orbit around the Earth. But it can’t be scientifically proven yet.
Hope that answers your question
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