
He took responsibility. He killed the child to save 1077 from his dark rampage. It worked. But now, he and 1077 are both guilty of killing. They will be punished, but I believe that 88 will reap the greater punishment, as he did it in his right mind 1077 went berserk (insanity defense equivalent). He's willing to take the risk and punishnment out of love and out of a sense of it being his fault for not managing 1077 better as his mentor/boss.

A little clarification. 88 isn't actually 1007's boss or anything, they're partners xD This setting is somewhat a crossover between the modern era and Chinese mythology where death gods are known as "Hei Bai Wu Chang". Otherwise categorized into "Black" and "White". There was no way for me to convey this in English, so I simply used "death gods"(I'm the translator sorry).
I guess you guys can say that this is somewhat shounen ai-ish. 88 and 1007 had a deep bond of sorts. In page 11, you notice that 88 said "the wrong job deployment was due to my negligence". But in the next panel, the other guy said that "no one has ever been able to change the King of Hell's mind when he makes a decision". In this context, it's more of 88 placing the blame on himself because he could have prevented it. We can infer from here that the King of Hell forced that job on them and 88 felt responsible because he was "negligent". Meaning he knew that 1007 was susceptible in influence could have exercised more caution to stop 1007 from going mad.
Here's what I understood:
These are death gods/shinigami/reapers. One of them has gone "dark"--rogue--and is killing people BEFORE their proper death date. He's become like a serial killer shinigami. So, two others are out to find him (one his previous mentor/boss and another shinigami with more clout, apparently, with the King of Hell).
It's implied that No 88 felt responsible for the Shinigami 1077 that went dark, because he put him on a dangerous case (I'm guessing reaping some murderer) and it turned his sensitive being dark. So, he wants to save him. When the other shinigami tracks him down, 1077 attempts to kill him to escape, but No 88 shows up and stops him. He has a child with him.
I assume this means that to recover his senses, innocent spirit power from a child is necessary. So, No 88 breaks the rules, risks hell and the great wrath of the King of Hell (moutain of needles, etc), by killing an innocent human for the sake of saving No 1077. The sacrifice works, but now his hands are bloody with innocent blood. He doesn't let No 1077 see the dead child.
So, presumably, they are either on the run together or No 88 willl take his punishment for the sake of No 1077.