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Is there a certain distance a C6 can be driven without the FOB being present?
I don't think so. You just can't restart the car without it.
A distance limit would kill the engine while underway, which would be unsafe. You'd lose power steering, brake boost, etc. It could quit on the train tracks.
People report driving dozens of miles before discovering the fob wasn't on board. From an anti-theft perspective, they might as well have gone a thousand miles.