Dead work is work done, by following after the laws, to gain righteousness (Heb 6:1 repentance from dead works; Heb 9:14; Rev 3:1-3). Dead work is useless work. Lots of effort but zero result. A monkey can behave like a man but that does not make it a man. A man can behave like a monkey and yet he remains a man. It is not by work to become but a transformation of new birth into a different kind that count. See "Be-Do-Have" of Grace Based Doctrine.
Fruitful work is work done according to the desire of God that results in many fruits that bring glory to God. We are saved for good work. The order is we must be saved first then we are empowered and led to do the right kind of good work. Eph 2:8-10.
Before our salvation, we try to gain righteousness by doing the right things. After a while, we know it is futile. We heard of the Good News of Jesus Christ and His completed works for us that we may become righteous not by our effort but by believing and receiving Him. We are born anew into righteousness and not by our work which is useless and dead in giving our righteousness.
After our rebirth with attribute of righteousness, we are called to do fruitful work. John 15:5 abide in Christ tells us how to do work that produce good fruit. John 15:16 tells us that our Father is glorified when we bear fruit. Gal 5:16 echoed the same method of "walk in the Spirit" that result in Gal 5:23 fruit of the Spirit of Love, Joy, Peace,.....
As born again Christians, we should not try to 'preserve' our Salvation by going back to follow after the laws. There is not need to as we who are born of Christ is already righteous(1 John 3:9). We are called to act out the internal reality of Christ in us Phil 2:12 by His grace (strength) Phil 2:13.
Related: Two Kinds of Knowledge