I've seen this several times over the years and have received numerous reason for the residue. With SMAW you will see this residue when welding with a long arc. Was told that this was from the Cr electrode and others from the flux. the remedy was to shorten the air, let the coating almost drag on the weld puddle. In TIG and MIG it is supposed to be because you loose the shielding gas for some peroid of time. This happens a lot on SS, again it the oxidation of the Cr. It is the same for the yellow fumes you sometimes see around welding. I've never seen anybody that seem to worry about it except to clean it off during after the weld was completed..
Though I've never analysed the residue I think the Cr idea is approaching the cause though I believe Fe enters into the picture because in a Steel mill a lot times you see yellow fumes prior to red fumes.
When we used to cut SS with an iron powder rig you would see yellow appearing fumes before the red cloud appeared.