What BY and HCK are teaching is that spirits (clay) during this probation period will be cast back into the furnace until it becomes pliable leading to the fulfullment of the prophecy that eventually “every knee shall bow and every tongue confess that Jesus is the Christ”. But, this is speaking of this probation period only.
However, universal salvation does not equal universal exaltation. All mankind will eventually be resurrected (just and unjust) and all will be offered salvation, but not all will be raised to the same glory. Not everyone who is saved will receive the same reward.
The sons of perdition are tragic suicidal spirits who eventually bend their knee to Christ and qualify to be saved but instead choose to cease to exist and choose to be completely recycled. However, unlike reincarnation, their being/essense is completely dissolved and the material is recycled into a new intelligence. God wastes not. But the new intelligence would have no memory of past existence. There is no “imprinting” of past lives on a new soul.
Think of your spirit material being thrown into a black hole, your essence completely dissolved, randomized and mixed with a trillion trillion trillion atoms, and then your energy being radiated back into space to eventually possibly combine into a new more useful form. But your previous consciousness will cease to exist “worlds without end”.
“They (sons of perdition) will be decomposed, both soul and body (body and spirit make up the soul) , and return to their native element. I do not say that they will be annihilated; but they will be disorganized and will be as if they had never been.” (Brigham Young, Journal of Discourses, 7:57)
This doctrine is not about reincarnation, infinite chances, or the wicked learning from past lives. Instead, this teaches that a few wicked sons of perdition will choose complete decomposition, dissolution, disorganization and disintegration. The sons of perdition are spiritually suicidal and even after bending the knee to Christ and confessing, these poor souls will reject any degree of salvation and instead choose nothingness— “the blackness of darkness forever”.