All we have that is authoritative in these matters is what revelation God has seen fit to give us. We can make some suppositions on the basis of that little bit of information, even speculate a bit trying to extrapolate from that data set, but we are beggars when it come to this subject. We have no means in ourselves to get the goods we seek. We can only receive that which the able and seeing has deigned to drop upon us as he's passed our way.
It seems to me, that at its core this issue comes down to properly understanding what it means to be made in the image of God. According to his word, we are the only thing created in the material world for which that description can be made. I think an argument could be made for at least some kind of angelic being fitting the description as well, since they are referred to as the "sons of God" in Job. So, humans and some angelic beings are made akin, reflective of the Father of spirits. What does that mean?
We are made with a sense of self, or personhood, along the line that the Lord God Almighty possesses. We will, choose, want, and create. It is what we've been made for. We're wisps of God's very breath, most assuredly, but that also means we are as indestructible in essence as is he. Can God destroy some aspect of himself? No, I do not believe he can--it would make him less God. Can God destroy some aspect of himself that he's leant to other creatures to live and be as they are? I don't think he can, and hence scriptures consistent testimony that the souls of mankind are eternal.
Annihilation is impossible because at our cores, we are not made of destructible stuff. The possibility of destruction disappeared when God decided to make us in his image and breathed into us the breath of life. Our living soul is made of the indestructible breath of God. We last forever, and God could no more destroy us now than he could destroy himself--that ship sailed at the creation. Even if our bodies disappeared in an instant, our souls would continue forever.
All that can be done with us for eternity is to immobilize us, segregate us, and then expose us to an environment that is so overwhelming that we have no ability to fill the spaces, all of which God is omnisciently aware of, with rebellious and evil thoughts. Generally, we refer to that reality as Hell. Now, some might question whether or not God could be that impotent in the face of his creatures. I mean, couldn't he make them be something else by fiat? Something more agreeable? After all, he is the sovereign Lord.
If God could have created something in his image that was that controllable, it wouldn't have been his image! In the end, whether or not something could be done another way by God is a silly question. The perfect God did what he did. Could it have been done differently? Perhaps. Could it have been better? Absolutely not! If there were some other way, some better way, for God to accomplish his ultimate aims, he would have done it that way.