Partnership dissolution asset distribution

All the liabilities must be paid off in full - there really are no rules because, if there aren't enough partnership assets to pay the liabilities, the partners must dig into their own wallets and purses to put in extra money to pay the liabilities What else do you think that you are missing here?

They have to pay all of it off? Is this because they do not have limited liability?

That's correct. And each partner is 100% liable so if one partner declares him/herself bankrupt, the others take on that partner's liability. If all the partners except one declare themselves bankrupt, the remaining solvent one has to pay 100% of the liabilities Ok?

Yes. It seems like risky business to me but I understand the logic.

It IS. A risky business - but that's the price you pay for trading as a partnership and having multiply fewer rules and regulations to comply with.