I've rigged a few models and automatic weights always worked pretty good, compared to what's happening to me now. Vertices assignment is all over the place and I don't know why. This happened only on 2.79 but it might be an accident. I know automatic-weights isn't perfect, but it used to work so much better in the past for me, way more accurately. Just asking whether maybe patch changed something, or did I mess some options?
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$\begingroup$ Can you upload the file? I recently had the same weird weighting occur and the answer was that my normals were pointing inwards in one segment which threw off the calculation. $\endgroup$ – Ben Dec 29 '17 at 10:26
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$\begingroup$ Look for (and fix) holes in the mesh. Automatic weights can "spill" out of these holes and contaminate other parts of the mesh from the outside. $\endgroup$ – Nathan Jul 3 '18 at 15:37
Happend to my model as well, exactly as you described.
Weighting couldn't be solved on the model, so I removed entire head and then applied armature with automatic weighting. Weighting was solved as in the bottom image (some weight, though not visible, was all over model). Then I removed eyes, glued head back to the body and weighting was solved normally.
I had bones sticking out of mesh when got this wrong weighting.