Golgithah heard rumors of a couple of squatters living in the unused shack at Mixwater Mill, so she went to check it out, expecting a fight to kick them off the property.
She was surprised to be greeted by a little girl who said she was hiding from "red and black monsters". She used to live at Honorhall Orphanage and has lots of awful stories about Grelod the Kind, but this man she didn't know (Griffith) took her away and into hiding. She doesn't understand why, but she's glad to be away from the Orphanage.
Turns out Griffith was member of the Dark Brotherhood until he was given a job he couldn't do--kill the little girl he's now protecting. The contact, a grown man, wanted her dead because she ignored his... romantic advances... and called her a harlot and all sorts of nasty things. But she's a little kid! Wtf, right?? So Griffith had a moral schism and killed the contact instead.
Unfortunately, once the Black Sacrament is performed it must be honored, so the Dark Brotherhood still pursues her and now also pursues the one who betrayed Sithis by killing the contact.
So Golgithah, ever the heroine, decided she would destroy the Dark Brotherhood. Before dragons, before anything else, she killed every last one of them that she could find. That's Astrid's clothing sitting on the floor next to him in the bottom picture. I tried talking more after the Dark Brotherhood was wiped out, but they didn't seem to notice and I had no dialogue options to tell them.
As a way of saying goodbye and good luck, Golgithah left a bunch of Dark Brotherhood armor (picked off the dead), gold, and a couple of necklaces in a chest for them. They didn't notice. But I like to imagine it helped them move on (even though Sithis haunts him and they're both still hiding in the shack)
This encounter was added by the fantastic Interesting NPCs mod.