I recently came across (paraphrasing) Das habe ich aus dem Hinterzimmer des Ladens mitgehen lassen. Apparently mitgehen lassen is an idiomatic and euphemistic way of saying "to pilfer". I'm wondering how the literal meaning connects to the idiomatic meaning. It sounds like the item followed the person out of the store like a lost puppy; is that a fair interpretation? There are entries in Redensarten-Index and English (not German, for some reason) Wiktionary, but neither gives any explanation for the origin.
to be dragged along with something else
is simply a literal meaning of "mitgehen", meaning 2.). Also frequently used to describe processes that have side effects.
Example, very up-to-date:
Bei dem Hochwasser gingen Sträucher, Bäume, Autos und sogar Häuser mit.
Thus "Das habe ich mitgehen lassen" simply translates to
I allowed or didn't prevent or used little effort that this one got dragged along with me
with "lassen" introducing a passive, trivialising aspect. It can have a few meanings in English, here an apt one would probably be "to allow".
In the end, it means
I stole this.
Wiktionary lists the meaning at least, but the corresponding lexeme page is not yet created.
Note, that mitgehen lassen as non-idiom means "permit sombody to walk with someone" (i.e. accompany him/her) and any corpora hit earlier than ca. 1970 is likely to have that "normal" meaning.
I had considered the idiom as not much more than an euphemism, downplaying the own participation in the theft, in the sense of "I did not reject something hopping into my bag".
I don't see a need to refer to "walking" instead of the more general "go".
gehen lassen is equivalent to let go, and the preposition mit implies a common direction.
The verbal phrase has a plain meaning: if a kid wants go with its friends to somewhere, the parents may let it, if the group will take it with them (compare mitnehmen).
A logical conclusion seems to be that it could be that it is ironic, self-reflexive, proposing command of the object to let it go. This might appear ironic or absurd.
It is offensive in the first place to assume command of the object, but the intent is usually kept secret in case of thieving. A thought crime, it is difficult to construct an Abstraktes Gefährdungsdelikt. Therefore, for all intents and purposes, everyone perceives the taking and going as infraction into somebody's possession, and calls it accordingly.
On top of that, lassen suggests that the action is effortless, as it should be to remain undetected.
That is to say, it only implies pilfering, as you say.
One might imagine that it had more basic implications, I'm wondering about dispatchers in logistics letting go a little extra for one reason or another, which might become collusion or criminal negligence to the detriment of the owner. Or it could be one of those infamous reinterpretations of Bargoens or other thieves cant, but that does not seem to be suggested. All things considered, it seems very literal.
Instead of a dog from a pet shop, it might also have referred to innocent children, I suppose, since kidnapping must have been rather lucrative at some point, in which case verleiten would have been a better choice of words, compare to lead, lead astray, lead away, but I can't quite tell if this is related or not (computer says no).