Berean Study Bible 2 Samuel 23:5
Is not my house right with God? For He has established with me an everlasting covenant, ordered and secured in every part. Will He not bring about my full salvation and my every desire?
What is full salvation?
I understand salvation--in the most complete sense of the word--to describe the effect of fully participating in God's plan of salvation. Let's break it down into several of its component parts to look at some of the promises God has extended:
Disclaimer: this is an NT interpretation of an OT text.
Forgiveness of sins
Come now, and let us reason together, saith the Lord: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool. (Isaiah 1:18)
That this is accomplished through the blood of Jesus Christ is taught in a number of passages; see for example Hebrews 9:12
Redemption from the Fall
After the Fall Adam & Eve were subject to death and were cast out of God's presence (see Genesis 3:3, 24). Redemption from both consequences comes through the atoning sacrifice of Jesus Christ:
For as in Adam all die, even so in Christ shall all be made alive. (1 Cor 15:22)
And Revelation 20 describes what follows the resurrection:
12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
Eternal Life
Becoming clean from our sins is very important, but alone it is not enough. To go through the exercise of life just to fall down, become soiled by sin, be forgiven, and remain as we were before would be a terrible waste. God has something more in store:
And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. (John 17:3)
And for their sakes I sanctify myself, that they also might be sanctified through the truth. (John 17:19, see also vs. 21-23)
And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together. (Romans 8:17)
God wants us to attain knowledge and sanctification and glory. The point is that we are to become something more as a result of the life He has given us.
And from 1 John 3:
2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.
3 And every man that hath this hope in him purifieth himself, even as he is pure.
If we say "I want God to forgive me but I don't want Him to change me" then we are completely missing the point. If we really understood what full salvation looks like, what that this earth offers could we possibly believe is worth more?
Conclusion
I believe full salvation includes all of the above. I don't think Jesus was kidding when He said "be ye therefore perfect", but it is not a commandment we will be able to keep on our own.
God intends for us to grow and develop and become. The atoning sacrifice of Jesus Christ does not merely overcome sin and death, it allows us to learn & grow from our experiences & mistakes, but not be damned by them. It is intended to change the very nature of those who fully accept it.
Full salvation is that which achieved by Jesus, "he is the mediator of a new covenant", Hebrews 9:15. All from ESV.
In the first covenant we have "the purification of the flesh" Hebrews 9:13.
But "the blood of Christ" is necessary to "purify our conscience". Hebrews 9:14
Another way of seeing this in Hebrews 9 involves "redemption/lytrosin":
In 9:12 " his own blood" has secured "an eternal redemption/lytrosin". Eternal and therefore "full".
But 9:15 "apolytrosin" is a full redemption and the added emphasis "apo" is necessary because "a death has occurred that redeems them from the transgressions committed under the first covenant". Hebrews 9:15.
The first covenant was not "full" as it was the blood of mere created "goats and bulls". Full salvation was secured by "his own blood". Hebrews 9:12.