The Kaliyuga is, especially by Puranic sources, considered to be the deteriorating state of humanity where ethtics, morality and intelligence are spiralling out of control.
For example, at the end of the Shiva-purana is told that the sages observed how this current Kali age slowly defiled everything:
Then Sūta blessed them and left. The righteous sages fixed their abode permanently at the outskirts of Vārāṇasī after performing the sattra at Prayāga when they perceived that everything was being defiled by the advent of the Kali age.
Presumably, those sages came into existence before the advent of Kali age.
What references are there for ascribing reasons to souls being born in the Kali-yuga? Is it based entirely on Karma? What kind of Karma? Are we supposed to gradually re-incarnate our way out of this kali-yuga?