Subjunctive Grammar

Subjunctive is rather insignificant in modern English. Most likely you might come across this form in American English, and most probably in formal texts.

Form

In most cases, subjunctive and indicative forms of a verb are the same. So often you would not notice whether a verb is used in subjunctive or indicative mood. The only indicator for subjunctive is that no ‘s’ is added in 3rd person singular and that the verb ‘be’ remains ‘be’ for all forms in present tense and becomes ‘were’ for all forms in past tense.

Use

Subjunctive is used in some fixed phrases (formulaic subjunctive).

• God save the Queen!
• Long live the King!
• Thy will be done.
• Be that as it may.

Certain verbs (e.g. demand, insist, recommend, suggest) and adjectives (e.g. essential, important, vital) are followed by ‘that’ + subjunctive (mandative subjunctive) to indicate that something must be done (directive aspect).

• People demand that the troops be withdrawn.
• It is important that everyone register.

Sentences in subjunctive sound very formal, however, so often an auxiliary is preferred. If the directive aspect of the sentence is clear enough without an auxiliary, it is also possible to simply use the main verb in indicative mood.

• People demand that the troops are / should be withdrawn.
• It is important that everyone registers.

But: Note the difference of subjunctive and indicative in the following example.

• She insisted that he be present. = She wanted him to be there. (directive aspect; subjunctive)
• She insisted that he was present. = She knew that he really was there. (observation; indicative)

In the example above, you can also see that mandative subjunctive is always used in infinitive, even if we talk about a situation in the past. Note that in negative sentences, the auxiliary ‘do’ is not used for subjunctive mood.

• She insisted that he not be present.

For wishes and hopes that cannot be fulfilled (volitional subjunctive), subjunctive is used in past tense. For all verbs (except ‚be‘) past tense in subjunctive mood is the same as in indicative mood.

• I wish, I had a million dollar.

Past tense, subjunctive mood for ‘be’ is ‘were’.

• I wish, I were a millionaire

Reference:
https://www.ego4u.com/en/cram-up/grammar/subjunctive