I continued my Internet search for a reliable source of information about stabistors, and I found a very old GE transistor manual (1964)
that answers most of my original questions, albeit briefly.
In chapter 17, titled
SILICON SIGNAL DIODES & SNAP DIODES, at page 450 there is the following section:
So, according to that source, stabistors (a.k.a. low-voltage reference diodes) have the following characteristics:
Physically they are silicon PN-junction devices, containing one or more PN-junctions connected in series.
Their forward VF – IF characteristic is tightly controlled (from process or post-production selection this is not clear, maybe both).
They are meant to be used only forward biased (confirming that they are indeed diodes whose forward voltage drop is used as voltage reference).
Their tempco is greater than that of a Zener diode, but this drawback is compensated by a tighter initial tolerance, lower dynamic impedance and absence of low-current noise. All this produces a more accurate voltage reference over the operating current and temperature range.
EDIT
The fact that a stabistor is probably not a particularly sophisticated device can be indirectly inferred by the following amusing anecdote, taken from this document:
Report to the Computer History Museum on the Information Technology Corporate Histories Project: Fairchild Corporation.
That is a collection of inside stories of Fairchild Corporation former employees, collected for their historical relevance in the development of electronic industry.
At page 85 there is this story (emphasis mine):
Title: Simpler Times and almost the largest diode order in history
Author: David Laws
I joined SGS-Fairchild in South Ruislip near London, England in 1966. After 2 years in marketing and sales, Bill Welling rescued me from a lifetime sentence of English weather and cooking in 1968 and hired me as a Headquarter Sales Engineer in Mountain View. My yearly salary was equal to that paid to the Prime Minister of England. Thank you, thank you, thank you, Bill!!!
My first weekend was spent at the Monterey Pop Festival enveloped in a cloud of strange, sweetsmelling cigarette smoke watching Janis Joplin and band members of Big Brother and the Holding Company down a whole bottle of Southern Comfort during an extraordinary twenty
minute rendition of "Me and Bobby McGee." The next week I discovered Bill Graham's Fillmore in San Francisco where Jimi Hendix was performing. Ken Kesey and the Merry Pranksters were terrorizing the residents of La Honda while Roy Kepler, of Kepler's Books, taught courses on nonviolence to the likes of Joan Baez. Around the Stanford campus, the Midpeninsula Free University offered a curriculum of bee-raising, bread-making, massage, meditation, psychedelic dancing, and yoga. A simpler but memorable era!
My job was to sell anything that was not bolted down to any customer who would pay money up front west of the Rockies. This included bent silicon wafers to National (Charlie didn't want to pay for straight ones) and out of spec packages to AMI. One of the more enterprising characters, Arnie Aplebaum, made a lot of money selling "repurposed" reject power transistors to the military. He sawed the top off the metal can, removed the die and then mounted two side-by-side onto a new header wired into a Darlington configuration. This device produced sufficient gain to ship against a mil spec that he had somehow managed to gain approval on.
I very nearly closed the largest diode order in history with Joe Patridge (I'm pretty sure that's who it was) who at that time worked for Burns and Towne. B & T had an operation that purchased fallout devices and re-screened them to sell to Hong Kong radio manufacturers. Those that did not work at all would be mounted in unconnected sockets on the pc board. These radios could then be advertised as 12 transistor models to consumers who did not know that only 6 or so of the transistors actually did anything. Anyway, back to the diode story. Ever since the diode plant had opened in San Rafael in 1959 reject devices had been stored in barrels in a warehouse next door. We estimated that these barrels held close to 100 million diodes. B & T knew that they could sell many of them as stabistors and reclaim the rest for their precious material content. We agreed a price that was approved by Tom Bay but by the time the P.O arrived in August of 1968 so had Hogan and crew. The new management thought that they could find a better deal and cancelled my potential historic order. As far as I know, when I left Fairchild 4 years later San Rafael was still paying to store the diodes in the rented warehouse.
While working on this deal I was taken on a tour of the San Rafael facility. It was a typical 1960's semiconductor plant where you could walk into the fab, test, and assembly areas in your street
clothes. The exception was the wafer sort station. There you were best outfitted with a pair of rubber boots. Test engineering had figured out that most electrical failures were caused by voids
in the die metallization. So rather than perform an expensive electrical wafer sort, they scribed the die and dropped them into a bucket of water. The metal voids trapped bubbles of air that caused
potential die failures to float to the top. These were skimmed off and the good die at the bottom moved on to the assembly line. Simpler times indeed!
Note: I quoted the entire story because it is amusing and really on topic wrt. electronics history, although not all parts are relevant to the answer.
That story tells us that at that time a stabistor could well be a rejected diode (so maybe not up to spec with their reverse max voltage or reverse leakage current) that could still be sold as a stabistor after a selection process.
So definitely not a specialty or exotic device at all!!!