Chip?! It's more like a plank. Slovenes, too, definitely have a love-hate relationship with those they call južnjaki / Southerners (when they're being polite). But I think the loss of the synthetic "pure instrumental" in Slovene is a little sad.
Well, actually SBC uses the instrumental the way it was originally used (and as it still is used in Russian and most other inflected Slavic languages): without a preposition; the case itself indicates the means or manner by which something is done. The Slovenes, probably influenced by the German use of the preposition mit to indicate means and manner, at some point started appending their own preposition "with", z/s, followed by the noun phrase in the instrumental.
Perhaps a better "literal" translation would be "following the bread on one's belly". It is sort of equivalent to the American expression, "to go where the money is", but the South Slavic phrasing is so much more vivid.