The yardstick for central bank "health" and/or "credibility" can be nebulous at times. It is sometimes argued that a balance-sheet assessment only does not capture the nuance of a central bank because the central bank's true "asset" is its ability to print money. But by the same token, central banks are now becoming bigger buyers of certain securities. In the case of Japan, the BOJ has over 50% of some maturities. The point being that when a central bank is expected to play a meaningful role when crises emerge, then it's "liabilities" will also be incalculable.
For commercial banks, equity serves as a quasi-clawback provision as it allows creditors to get repaid should the bank encounter extreme solvency issues. But for central banks, I'm not sure what "equity" really signals to anybody.
At what point does negative accounting equity register on the broader macroprudential radar and why? I suppose that even though one cannot have a "run" on a central bank, it could be seen as a BOP or FX crisis.