Was your friend already "asleep"? Because when you are asleep against Freddy you have the Oblivious status effect on you, and there is no terror radius, so perks affected by terror radius don't work including Borrowed Time.
And don't forget when you are hit by Freddy you are automatically put to sleep, so it's not possible to take the hit then unhook and rely on BT.
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This isn't a bug, if your friend was asleep (which he must have been) borrowed won't activate because the lullaby isn't a terror radius.
Was your friend already "asleep"? Because when you are asleep against Freddy you have the Oblivious status effect on you, and there is no terror radius, so perks affected by terror radius don't work including Borrowed Time.
And don't forget when you are hit by Freddy you are automatically put to sleep, so it's not possible to take the hit then unhook and rely on BT.