Shadow probably refers to a part of the unconscious mind that symbolizes repressed weaknesses or faults, as outlined by the Swiss psychiatrist Carl Jung. It could also be related to a kind of ghost called the Shade.
A Shadow is first encountered in Mazurka Corridor on the 7th floor, where a man will beg Akemi Nakajima for help and ask for a weapon. Regardless of the answer given, he will transform into a Shadow and attack.
Shin Megami Tensei III: Nocturne
"It can transform into any person it sees. It is said that whomsoever meets it will die within a few days, and much folklore stems from this creature. They may also become physical incarnations of psychological ailments."
—Shin Megami Tensei III: Nocturne compendium
Shadows appear as medium-leveled demons which the Demi-Fiend encounters after his transformation into a demon. It can easily be found in the Tower of Kagutsuchi. Being a Foul Race demon, the Demi-Fiend can only interact with it during the Full-Kagutsuchi phase or by having the Jive Talk conversation skill.
Shin Megami Tensei IMAGINE
Shadow can be contracted in Ueno at night and in Ichigaya Camp's silver-level instance.
Devil Summoner: Soul Hackers
"A phantom that appears as the person who sees it. It is said those who see it will die within a few days. There are similar tales around the world, and some of these cases of sightings have been reported by mentally ill patients."
—Devil Summoner: Soul Hackers 3DS compendium
Shin Megami Tensei: Liberation Dx2
"A ghastly being that appears in mirror image of its victims. It is rumored that within a few days, death will come to those who see them, There is much lore in multiple cultures pertaining to this phenomenon. Some say that it is a sign of mental illness."