The human will is what needs to be saved and I have a news flash for you, it cannot save itself nor can it ever be saved. It is in slavery to a fleshly nature (heart/mind) so depraved that Paul says even as a saved man "there is NOTHING good in my flesh" and the "will" of the flesh continues to operate as an unchangable "law" which even a saved man has no power to over power its "will" for sin:
For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
19 For the good that I would I do not: but the evil which I would not, that I do.
20 Now if I do that I would not, it is no more I that do it, but sin that dwelleth in me.
21 I find then a law, that, when I would do good, evil is present with me.
The only way that even a saved man can overpower the "will" of the fleshly nature is by the Sovereign will power of God - "For it is God that worketh in you both to WILL and to DO of His good pleasure" (Philip. 2:13).
There is no salvation for the "will of the flesh" but God gives ANOTHER NEW HEART with a new "will to do good" (Deut. 29:4; Ezek. 36:26-27). However, the new heart with the new "will" is powerless to overcome the will of the flesh.
For I delight in the law of God after the inward man:
23 But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members.
24 O wretched man that I am! who shall deliver me from the body of this death?
25 I thank God through Jesus Christ our Lord. So then with the mind I myself serve the law of God; but with the flesh the law of sin.
The Spirit of God ALONE without any aide whatsoever from the elect creates the new heart with a NEW WILL that battles against the will of the fleshly heart/mind and which works cooperatively with the Holy Spirit in defeating the will of the flesh.
There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit.
2 For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.
3 For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
4 That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
Therefore, the distinction between the saved and lost is not the fleshly nature and its will for sin. The difference is that the saved man has a dual nature and the additional new nature predominates the mind ("the law of the mind") even though it has no power to overule the will of the flesh ("the law of the flesh"). The lost man lives "walks" and is totally controlled by the "mind" of the flesh. The saved man is not totally controlled by the "mind" or will of the flesh but the new nature predominately controls the mind and is thus spiritually minded and as empowered by the Spirit "walks after the Spirit." Remember, Paul said "So then with the mind I myself serve the law of God; but with the flesh the law of sin." The saved mind predominately "minds" the things of the Spirit:
For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit.
6 For to be carnally minded is death; but to be spiritually minded is life and peace.
7 Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.
The lost man is wholly and totally "in the flesh" and predominated by the law of sin whereas the saved man is "in the Spirit" simply because he has a NEW "inward man" born of the Spirit that predominately minds the things of the Spirit and is victorious over the flesh when empowered by the Spirit:
8 So then they that are in the flesh cannot please God.
9 But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his.
Willingness to be free from the power of sin must be created by God and even when God gives a new heart with a willingness to be free from sin it is powerless to overpower the will of the flesh. The will of the fleshly nature is never destroyed until the body dies and it is only subdued progressively and partially from the new birth until death or glorification.