Had they? I'd have to see some evidence of that. Lincoln promised strengthened fugitive slave laws.
Of course we know slavery was safe within the union. Nobody thought the federal government had the power to ban it and there were enough slaveholding states to prevent the passage of any constitutional amendment that would have banned it. There was a fugitive slave clause in the Constitution that protected slave owners. For any state that seceded however - assuming it be allowed to depart in peace - slavery was doomed and quickly. The US would immediately be a foreign country with no obligation to return their escaped slaves.
Absent the restraints of Northern public opinion, slaveholders expected that the Confederacy as a whole would be more diligent and effective in controlling their slave population and preventing them from fleeing captivity.