What is this formal (perhaps old-fashioned) actual-state-of-affairs use of 'should' called?

Here are three examples of the kind of thing I have in mind:

• “That he should do such a thing is terrible!”
• “That this should be the case is regrettable.”
• “That such a thing should happen is a blot on justice.”

In these examples, the ‘should’ is clearly not playing a commendatory role. Nor is it referring to purely hypothetical states of affairs, as in a conditional sentence (e.g., “Should such a thing occur, it would be terrible”). Instead, the ‘should’ is used in a construction that introduces an actual state of affairs, which in these examples is then negatively evaluated. (Of course, one could do the same thing with a positive evaluation—e.g., “That he should do such a thing is wonderful!”—but then you might mistakenly think the ‘should’ is commendatory.)

Does anyone know how grammarians or usage experts refer to this use of ‘should’? Ideally, I’d like a term I could plug into Google for further research. Thanks!