I think you're mistaken -- seigniorage is the difference between the cost and the value, it doesn't need to be a profit. Negative seigniorage is still seigniorage and many such papers treat it as such, e.g.;
>Negative seigniorage is still seigniorage and many such papers treat it as such
Notice how you qualify your statement as many such papers treat it as such.
Yes, you can find some people, articles that refer to a loss as seniorage, but that’s a misuse and inconsistent with the actual definition. That’s also why when they do use the term improperly they typically add “negative”, specifically because the definition of Seniorage refers specifically to revenue/profit from printing money.
https://sci-hubtw.hkvisa.net/10.2307/3552184