The speaker looks back on a shared life and sees it as flimsy and provisional. "We have been thin paper in the rough draft of our lives" suggests people who never got to write the final version: everything feels like a first attempt, easily torn, never polished. The "we" matters here. This isn't one person's complaint but a collective voice, which hints at a group of people who have had little control over how their lives turned out.
The second stanza sharpens that feeling. Even "our greatest word", the best thing these people can say or promise, is compared to a contract for "our share of coal." That image is small and bleak. Their highest ambition is a bargain for fuel, a bit of warmth or survival. The poem doesn't spell out who holds the power, but judging by the imagery, it seems to be someone else. The mood is quiet, tired, and a little bitter, with a sense of making do on very little.