Eternal deliverance was accomplished on the cross for all of those that God gave to Jesus to die for, which had nothing to do with any action on the part of those that he died for. It was totally by God's sovereign grace, without the help of those he died for.1 Cor 1:21 - For since in the wisdom of God the world through its wisdom did not know him, God was pleased through the foolishness of what was preached to save those who believe.
Preaching of the gospel of Jesus Christ can be responsible for saving (delivering) those that he died for from believing in the letter of the old law to save (deliver) them eternally, by their good works. This is a deliverance that they receive as they sojourn here on earth. Preaching of the gospel cannot deliver anyone eternally.
God's instructions to his ordained preachers, is to teach the lost sheep, of the house of Israel (not all of the nation of Israel, but Jacob/Israel, which is God's elect (Rom 9:11), teaching them the knowledge that Christ has already paid for their sins, and not to depend upon the old law for their eternal deliverance. therefore, saving (delivering) them from their ignorance. Romans 10 is a good example of delivering those that believe in God, but not understanding what God has already done for them.
If you believe that all of the salvation (deliverance) scriptures are referring to eternal, the you are believing eternal deliverance is accomplished by your good works.