It seems that the "cure" for the disease in Willenberg's case is not a result of HIV's genome getting "trapped in genetic prisons", but is actually conferred by immune cells that kill off any and all cells which attempt to replicate it. A quote from the article:
"They suspect that, in some people, immune cells known as T-cells target and kill infected cells that carry HIV in easily-accessible portions of the genome — in regions where it can be copied."
Such infected cells would be capable of some level of HIV replication, or present viral antigens on their surface, thereby exposing themselves to immune surveillance and elimination, at least in Willenberg's case.
If so, the "cure" is not established by sequestering the genome in inaccessible areas, but rather by an active cellular immune response that destroys any attempt to make the virus by cells not "locked down". The presence of the HIV genome in "locked regions" after a "cure" is merely a default condition, and has no actual relationship to any "cure".
Again, the "cure" it would seem is inferred by a unique immune response not seen in most people. In Willenberg's case, she had an effective subset of T-cells that allowed her to minimize viral replication by killing off any cells actively producing virus, or preparing to do so. "Locked out" HIV genomes are merely the end result of such a cure - with no HIV expression, there is no "reason" to kill those cells.
Extended antiviral therapies might allow some people's cellular immunity to slowly develop an equivalent mechanism of killing all cells that try to make the virus, leaving only "locked out" cells as the only source of the viral genome. Those "locked out" cells may never be eliminated from the body since they never draw attention from immune surveillance because they never attempt to produce active virions.
So it would seem that it is not the "lock out" of the HIV genome, but rather the elimination of all cells where it is not "locked out". Cells that sequester the genome spare themselves from certain death, and are not related to any "cure". Should any of these "locked out" cells change and begin to replicate the virus, they would be killed off by the T-cell response, the means by which a "cure" is actually established in people like Willenberg.
As long as such T-cells remain active, the "cure" is likely too remain viable, assuming that complete viral elimination is never attained since there is evidence of a continuous low level virus production in most people who are infected regardless of immune competence, or for those who are on antiviral therapies.