The Chatsworth paternoster, for instance, once owned by Henry VIII, was clearly designed that way; we can tell because the program of carvings includes complete "sets" of motifs -- all twelve apostles, for instance. If there were originally more beads, some "sets" would probably be incomplete.
On the other hand, one of the tenners featured in Eithne Wilkins' The Rose-Garden Game made me think twice.
In its current form, this is composed of twelve beads carved (or so it's said) from apricot kernels, and a tassel (the funny-looking thing on the end), with what look like silver-gilt and enameled beads and small pearls in between. The beads are fairly typical of rich rosaries of the late 16th century, and the tassel is black enamel and gold with five chains of small pearls and turquoises. It's probably Italian and dates to sometime around 1560; it's now in Munich (Treasury of the Residenz). So at first sight there's not too much that's odd about it.
But why twelve beads? Most rosaries, even the short ones, seem to be in multiples of 10, 50 or sometimes 5. Offhand the only devotional practice I can think of that goes in 12s is the daily prayer of members of the Secular Franciscans, who are supposed to say twelve Our Fathers each day, as a substitute for the psalms recited daily by the friars. (I have actually made myself a "twelver" specifically for this.)
It's possible, however, that what we're really looking at here is an accidental number twelve: the remains of a longer rosary that has broken, and it has either been shortened to produce a more practical number, or perhaps, just kept in someone's possession for the sake of the special beads.
My clue that this might be the case is a close look at the photo of the end of this string, the one not attached to the decorative tassel. I can see what looks like a loose end of the cord on which everything is strung. If this had been designed to have exactly twelve beads, I'd expect to see something attached to the other end, probably either another tassel or a ring. This looks more like a broken end to me.
I don't know if anyone's made a study of this piece, but I'd be interested to see what they said if so.