Interestingly enough the Synod of Laodicea (accepted by the EO, don't know about OO) forbids subdeacons the orarion and Byzantine ordination rubrics calls the subdeaon's vestment a cincture which like the little phelon of the reader is used only at ordination. (Somebody posted pictures of this at byzcath) The subdeacon assumes the crossed orarion in contravention of the canon afterwards.
The canons recognised by Syriac tradition include canons prohibiting stoles to subdeacons and readers as well as canons allowing them.
Technically speaking, Armenian subdeacons (literally rendered in Armenian as "half-deacons") should not wear the stole over their shoulder. Rather, it is worn folded in half over the left forearm. At the ordination, the stole is laid over the arm, and is supposed to wear it that way until/if they're ordained a full deacon. For me, I wore it on my arm the day I was ordained, and like everyone else, just started wearing it over my shoulder thereafter. It was just an unspoken understanding. When I was ordained a deacon, I wore it over my shoulder until the ordination began, and then moved it back down to my arm. Some places still do it in the traditional way, but it's not that common. Frankly, it's really
difficult to do anything with the stole just hanging half-folded over your arm like that. Incredibly impractical.
There was also a minor craze in the United States back in the 70s and 80s for ordaining "stole-bearers," a kind of middle ground between the four minor orders (tbir, or clerk/acolyte) and subdeacon. They'd wear stoles, but with the same color robes worn by the acolytes/choir, rather than the deacon's robes (in most parishes I've been around, deacons wear blue, choir wears red, though sometimes that's reversed). It was more an honorary thing for longtime altar servers than anything with defined duties, and didn't really have a canonical basis, either. It's not that common anymore, if even done at all, though there are still a few now-middle-aged-to-elderly stole-bearers floating around out there.