A TL;DR of the book (still read it!) is that debt was (at least typically, and as best we can tell) around before money, and that early communities operated on

A TL;DR of the book (still read it!) is that debt was (at least typically, and as best we can tell) around before money, and that early communities operated on debt internally and mostly used barter or money-like things when dealing with dangerous, untrustworthy "others", which turns the usual "first we bartered, that sucked so we invented money, then debt" narrative around. Something really resembling money, it claims, didn't come around until rulers invented it to better fund their armies ("OK, soldiers who will be operating in areas where you don't have social ties, here are five coins. All you civilians, including the ones we just conquered? You're each gonna need one of those coins to pay your taxes next year, or I'll take all your shit. Boom, now the coins have value.") The book advances the idea that barter is most common as a temporary measure among people who are used to using money but, for a time, cannot (during prolonged disasters, in prisons), not as a major feature of the economies of early or primitive societies. It also ties the collision of debt-and-money with social-debt societies to the development of slavery, and covers a bunch of other interesting territory. Again, do read it. As for negative numbers, you can express "owes" without them so I doubt it was a problem. After all, you don't "owe" someone negative one thousand dollars—you just owe them positive one thousand dollars. You hand them a negative-one-thousand dollar bill, they're not gonna be happy. Being able to write negative balances or work formally with negative numbers isn't strictly necessary to work with debt.