It's not like there wouldn't be any more cattle ranchers. If say a subsidy on cattle production were removed today, the ranchers would refuse to sell to restaurants and distributors at the low price they do today and agree on some price they can break even at. Anywhere offering burgers would have to do it at a much higher price to break even. Many less consumers would likely choose to purchase them, decreasing the demand for burgers, causing a decrease in demand downward until things balance out.

Related would be the conflicting effects on supply of less economies of scale vs being able to utilize only the most efficient means for production (e.g., only the places most fit for it would be producing cattle, meaning that the marginal cost would be lower than in the previously utilized high cost areas, although this wouldn't be sufficient to counteract the original shock, it might help balance the other effects.)

It would start further up the chain with commodity farmers providing the feed.

Ok, true. But regardless of where it starts, there would not be one spot where one part of the chain was making some huge profit. Thus, it wouldn't be as the parent poster suggested (for the feed producer or the cattle rancher).