This meant that they could no longer retain immortality in their mortal bodies.
"And the Lord God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever: Therefore the Lord God sent him forth from the garden of Eden." (Genesis 3:22-23)
This is said to have been 'merciful' on God's part - that if they were still immortal in their fallen state, they would be unredeemable, just like the Fallen Angels.
If one is immortal and in a fallen state, then such a being will always stay the same as they are and either can't - or won't - change.
This helps to explain why the fallen angels, and perhaps their offspring (the nephilim), are likewise unredeemable.
And further, why those who take the Mark of the Beast are condemned. The 'mark' must also convey immortality, as in the verse where it says:
"In those days men shall seek death and not find it; and shall desire to die, and death shall flee from them." (Revelation 9:6)
Those who take the Mark of the Beast won't be able to die, but will wish that they could.
Even now there are those who are seeking immortality, either through 'science' or sorcery. Many of these persons seem to be either God-haters or God-deniers.
They themselves have already realized that they are in a fallen or 'debauched' enough state that they are unable, or at least unwilling, to let themselves be redeemed by God.
Their conscience must already be 'seared with a hot iron' and they want to find a 'different way' than God's way to eternal life: to try and "climb up some other way" into the sheepfold.
So much of that is already being attempted even in our current day, especially with all the new bio-technologies such as cloning, gene therapy, and genetically modified foods.
It's interesting, too, to ponder the biblical tie-in with " trying to climb up another way" into the 'Sheepfold', and Dolly the 'Sheep' (the first mammal ever cloned).
"He that entereth not by the door into the sheepfold, but climbeth up some other way, the same is a thief and a robber." (John 10:1)
"For as in Adam all die, even so in Christ shall all be made alive." (1 Corinthians 15:22)
"Lift up your heads; for your redemption draweth nigh." (Luke 21:28)