The total part of total depravity simply means entire. That is, in the fall, every aspect of man was corrupted, and not that every facet of man was utterly corrupted.
Then, if that were accurate?
Then there would be nothing that God could save.
Its only the soul He saves.
Not our flesh.
It is the fallen nature of the flesh that corrupts our soul's actions, like too much alcohol corrupts the performance of our body.
Sober up that body?
And you are safe to drive.
Likewise...
Apply the power of grace to our person?
We are safe to walk in righteousness.
The soul is dependent upon what rules over it.
By default, when the soul free of the fallen flesh? It is not automatically depraved.
Nor, is the soul righteous without the right rulership of the Spirit.
We must differentiate between the condemned flesh that forces our souls to sin.
And, our same souls?
That when under the grace of the Spirit?
Will not sin.
And, if we should slip up and sin?
Instant cleansing, with 1 John 1:9.
The Soul's volition determines what campground it will set up it's tent in.