Maximizing yield of inedible roots

Magnanimously indulging the almost worldwide delusion that cassava is edible, I look instead at things that (1) are in the ground and attached to plants and (2) if you pull 'em out, you can sell 'em to people who would never dream of putting 'em in their mouths. Offhand, though, the only such thing I can think of is the grass that is the source of vetiver oil, and the only reason I can think of it is I came across it in one of J.W. Purseglove's magisterial texts on tropical crops. I'm not thinking of yams, because (1) Purseglove archly points out they "can be used as foods in times of famine," (2) when less desperate stomachs and minds are considering a role for them, it is as the great source of diosgenin, the starting material for just about all industrially produced sterols, such as birth-control pills, and (3) even if you're just shoveling the damned things into locomotives, they still make big lumpy organs you can lift out of the ground.

So, what about root crops with roots you can't lift out of the ground? Imagine a valuable but determinedly fibrous root: you want a lot of it, but if it spreads deep or down, that makes it harder to harvest in full. Is it economical to confine those roots to some machine-accessible zone? If what you're after is fiber and these hypothetical roots are rope-strong, it may not matter where the things have wandered off to. You pull as hard as you like and they always answer. But I'm imagining that isn't the case - there is little need for deep roots to be built out of long and lignified cells, and as far as I know this doesn't happen. Such roots must have something else of value in them. Whatever it is, how do you maximize yield, recoverable yield, of them?