There are some Proof of Reserve schemes that people have been kicking around for a while. That would be hard proof that the mint has the BTC (or whatever).
Also Calle has this Proof of Liabilities scheme.
https://gist.github.com/callebtc/ed5228d1d8cbaade0104db5d1cf63939
Ideas... none of them are implemented anywhere yet as far as I know.