Take Bitcoin for example. It's a financial asset to whoever holds it. To whom is it a financial liability? I suppose you could say "it is a liability to the whole community of those who accept Bitcoin in exchange for goods". But that answer seems like a desperate attempt to salvage the assets=liabilities dogma. Nobody is obligated to accept Bitcoin.
Here's the right way to think about it. It's quite simple really. Very basic economics.
Suppose I sell you my car for $2,000. That would only happen if I value my car at less than $2,000, and you value my car at more than $2,000. So when I sell you my car, it must mean that the value of the car increases.
Only in a perfectly competitive market, where I and lots of others are selling lots of identical cars, and you and lots of others are buying lots of identical cars, and each buyer and seller takes price as given, does the value of the marginal car to the buyer equal the price, which equals the value of the marginal car to the seller, so the sale of that marginal car creates no net value.
Now suppose it's not a car that I sell you. Suppose I sell you a bit of paper on which I have written "I promise to pay the owner of this bit of paper $100 on 9 December 2017 signed Nick Rowe". The only way I would sell you that bit of paper and you would buy it is if the value of that asset to you is worth more than the value of that liability to me. So when I sell you that bit of paper, your asset > my liability.
Now suppose that my IOUs are more liquid than your IOUs. Because everyone recognises my signature and knows what my IOUs are worth, but I'm the only person who recognises your signature and knows what your IOUs are worth. A more liquid asset is more valuable than a less liquid asset, other things equal, to those who value liquidity. So there may be gains from trade if I sell you my IOU in exchange for your IOU. And if we do voluntarily swap IOUs, it must be that we create value by doing so, so that aggregating you and me, our combined financial assets > our combined financial liabilities.
See how easy it is? It's just like me selling you my car.
Now take the limiting case. Make the IOU that I sell you have a longer and longer maturity, approaching a perpetuity that pays an annual coupon. The greater the liquidity of that IOU, the lower the coupon I need offer to persuade you to buy it at a price of $100. If it's liquid enough, I don't need to offer you any coupon at all, and can stretch the redemption date out to infinity. It's an asset to you, but not a liability to me.
In fact, if it's liquid enough, and if you and the people you might sell it to value liquidity enough, I could even make the annual coupon negative. It's an asset to you, and an asset to me.
And in real terms, adjusting for inflation, paper currency is just like that. It pays the owner a negative real (inflation-adjusted) yield.
But, at the margin, money is only net wealth if the issuer has some sort of de facto or de jure monopoly power. Just like the sale of the marginal car creates no value in a perfectly competitive market. Which is what Pesek and Saving said back in the olden days. And it's all based on what the Austrians (and others) said, even earlier. Value is subjective.
Don't get muddled by accounting. It's just a way for me to keep track of how many cars I own. Just like a supermarket keeps a record of how many cans of beans it has on the shelf.
Update: Anwer Khan (deepwatrcreature) Tweeted: "it is net wealth due to the network effect. The surplus goes to those who establish the network, e.g. "exorbitant privilege". And I replied "Yes. Network Effect both creates Liquidity AND creates First Mover (incumbent) Advantage for de facto monopoly."