It was inevitable, and apparently it was already in action before the media reported it. When Jang Song Taek was nearly frogmarched out of the conference hall, one night after his execution, police were dispatched to collect his immediate family and blood relatives and truck them out to a prison camp.
Uncle Jang’s record was not clean, granted: he attempted to solidify his power base in 2004 and was dethroned for it, but managed to win his way back into the KWP’s good graces through his innate charisma. But even for upright, absolutely loyal citizens and party members, once the administration decides you are a traitor, they condemn you right down to your genetic code. You are considered to have a traitorous gene, one shared by your family.
This is slightly different than Pol Pot’s policy of executing the family of his political targets: in that situation, he was simply trying to preclude anyone coming back to seek revenge for the death of a loved one. In North Korea, on the other hand, Kim Il Sung established the belief that there is a latent proclivity for treachery in all the victim’s relations, both present and two more generations hence. If you were a loyal party member and your grandfather was determined, even posthumously, to have been a traitor to the state, you would be prison-bound. After that, somehow, the genetic slate is scrubbed clean and the relations, if any, are permitted to rejoin respectable Korean society.

All of this takes place in the labor camp, mind you. Uncle Jang’s relatives are already imprisoned, any potential nieces or nephews he and Kim Kyong Hui had will be imprisoned, and any children they manage to have (in secret, of course) with anyone else in camp—for love and the indomitable human spirit yet smoulder even in this oppressive Orwellian regime—will also be culpable. In fact, a worse fate awaits those born in these prison camps: they are raised as personal slaves to the guards. This is the testimony of Shin Dong-Hyuk, born in Camp 14.
One pertinent question here is, what will happen to Jang Kim Song? The last I was aware of, he was working in the Central Committee of the KWP as an aide to his father, until Uncle Jang’s demise. Being that Kim Song was so low-key and obscure from the political camera, I have to assume he has been carted off to prison without fanfare or ado. See, it’s not enough that Kim Song had been a loyal party member up to this point. It doesn’t matter that he swore to serve Kim Jong Un and the KWP. It doesn’t matter if he had a spotless record or even if he had been personally commended by Supreme Leader at any point. More prominent figures than he have been shuttled to the labor camps once the treason-by-proxy gene was revealed.
For this reason, I assume Jang Song Taek’s family was watching his career with greater-than-normal interest. I wonder if they sweated it out when he attempted the coup in 2004. I picture them glued to the TV and newspapers for every little thing he was up to, because his fate would dictate theirs.
Note: I’ve attempted to reach, via Twitter, a dozen experts on North Korea studies pertaining to Kim Song’s fate. I’m pretty sure he’s in prison, but I would like to know whether they have better intel or if it’s simply impossible to ascertain.