I'm adding a picture that I found in the archives.
The picture is mine, posted for opinions about whether the "blue
quartz" is dyed.
In this case, I string the beads on the 1mm snake chain-- then slide
them up out of the way while I melt the ends. No problem.
I have experimented a bit with melting balls on wires close to
stones-- I remember a workshop, early in my career as a jeweler,
from a woman who claimed to do this with pearls! In all my attempts,
I got one success, and many burned pearls. This was using a Little
Torch, which has a very tiny, very hot flame.
I have succeeded with a few stone beads such as hematite which are
not sensitive to heat. Others, like ocean jasper, stayed intact but
changed dramatically in color (to pink and orange). By the way,
hemetite stays very hot for a very long time (sad voice of
experience, scars to proove it).
I think this is a very difficult-to-impossible thing to do, most of
the time. I was hoping someone would post a different response... If
you can set up your piece so that the stone is in water, and you use
a tiny, very hot flame, you might be able to pull it off.
Let us know how it goes!