If we ignore that:
Dumbest version: You give everyone a list of all the liabilities. They make sure they are in there themselves. Anyone left out isn't entitled to the assets in an insolvency, so there is an incentive to check.
This isn't very efficient, giving everyone the whole list. But make a hash tree with each node carrying a hash and the sum of liabilities below it. Show each user their log2() sized proof. Much more efficient.
This leaks information about the distribution of ownership. Replace the values with pedersen commitment (and range proofs on their sums), and only open the top and bottom ones.
There is a fine writeup on the subject here: https://web.archive.org/web/20170928054354/https://iwilcox.m...
(Archive.org link because Zak died a couple years ago stomach cancer at age 40 due to an undetected chronic H. pylori infection, and his website didn't out survive him for long)