According to Abhidhamma exegetical texts, meditation of the 4 types of sense-sphere functionally inoperative-indeterminate cittas associated with wisdom (paññā) leads to knowledge of purity (vodāna), issuing in the supramundane Path-cittas of Once-returner (Sakadāgāmi) and Non-returner (Anāgāmi).
That's incorrect and impossible. 8 Mahakiriya-Citta can not arise with Puthujana, Sotapanna, Sakadāgāmi, and Anāgāmi person.
All 8 functionally inoperative-indeterminate cittas (maha-kiriya) can arise only with Arahanta person.
4 wisdom purity-cittas (vodāna) can arise only with Sakadāgāmi and Anāgāmi person.
What about the other 4 types of sense-sphere functional-indeterminate cittas that are dissociated from wisdom (paññā)? Since these four types of cittas are not conjoined with wisdom (paññā), do they still lead to the concentrative stage of purification (vodāna)? And to Nibbana?
Vodāna is not functionally inoperative-indeterminate cittas (Maha-Kiriya).
Vodāna is 4 Wisdom Sense-Sphere Wholesome (Maha-Kusala).
If those four types of citta do not lead to purification (vodāna) and subsequent Nibbana,
"Lead" in Vodana's condext means arising-citta before Magga-citta.
G: Gotrabhū for Puthujana or V: Vodāna for Sakadāgāmī/Anāgāmī.
See more: http://www.palikanon.com/english/sangaha/chapter_4.htm
If those four types of citta do not lead to purification (vodāna) and subsequent Nibbana, and neither do they also generate rebirth kamma-deposits,
Vodāna generates rebirth kamma-deposits because it is Maha-Kusala. It is not functionally inoperative-indeterminate cittas.
then when the living Arahatta person dies, where will be the destiny?
No where. All of Arahatta's aggregates is vanished by no left craving of senses, being, no being.
Will that person be born again as a living Arahat?
No, all of Arahatta's aggregates is vanished after death, but the other still rebirth after death. And there is no person everywhere from start. There is only craved depending aggregates which wrong view think "this is real controllable person" but actually it is just depending on many origins, no one.
or does he become an achiever of only Arahatta’s Path but not of fruition?
There is no Arahatta's aggregates after his death. And there is no Arahatta from start. The achieved aggregates and after that are called Arahatta.
For the description:
PaAuk Tawya Sayadaw Nama Rupa Description