Such a clause may be dependent on verbs like insist, suggest, demand, prefer, [a] adjectives like necessary, desirable, [b] or nouns like recommendation, necessity; [c] it may be part of the expression in order that… or some formal uses of so that… ; it may also stand independently as the subject of a clause or as a predicative expression.
The second, however, expresses a counterfactual circumstance connected with the present, and therefore contains or should contain a past subjunctive. If I were a cat, I would lie in the sun all day. This shows a wish or doubt.
The phrase as it were, however, cannot be modified: Having to ask permission, as it were, to see her friends Suddenly, as it were overnight, the weather became hot and sultry. It was as if Sally were disturbed in some way.
Note that the subjunctive does not change according to person I, you, he etc. All entries conclude with a section highlighting why the grammar point is relevant for a writer and top-level bullet points summarizing the entry.
We asked that he carefully to the directions before starting the project.