Very near the beginning1 of Fate/hollow ataraxia (the sequel VN to Fate/stay night), Mitsuzuri tells a ghost story to an audience including Makidera Kaede, Sageusa Yukika, Rin, Sakura, Issei, and Shirou.2
The gist of the story is basically what the Type-Moon wikia says on the page for Mr. A - some dude named "A" lives next to a little red-hooded girl whose parents are abusive. One day, the girl's parents are found murdered, and the girl herself is nowhere to be found. Later on, a spoopy apparition of the little girl appears before him, and drives him mad.
This little girl is also alluded to in Fate/strange fake - F/sf's "player" character is explicitly named "A" at one point, and his backstory matches up with the story told by Mitsuzuri in F/ha. The text indicates that the player character will sometimes see visions of a bloodstained little girl, who is presumably this little red-hooded girl.
I'm not sure where that picture comes from, though. The PS Vita release of Fate/hollow ataraxia just came out last week; maybe it's one of the CGs from that.
1 I haven't played F/ha, but I have had the pleasure(?) of looking at the .po files for it; this particular scene occurs in
真・冒頭-08, which I would estimate is about 20 minutes from the beginning or thereabouts.
2 Mitsuzuri, Makidera, and Saegusa appear a lot more frequently in F/ha than they do in F/sn (where they're basically background characters that vanish after day 3-ish of the VN).