Learn English – “used to always say that” or “used to always to say that”

Never may either precede or follow a tensed auxiliary.

The ordinary position, as you know, is after the auxiliary.

He will never agree.
I have never liked sushi.
She will never be mine.

But in parallel clauses like this, never is usually placed before the auxiliary; this throws the stress onto the auxiliary and thus emphasizes the contrast in tenses.

He has not agreed, and he never will agree.
She is not mine, and she never will be mine.
I don't like sushi, and I never have liked sushi.

Note that the parallel clause need not occur in the same sentence; the speaker may ‘pick up’ a phrase to parallel in the previous sentence.

A: John has never agreed to proposals of this sort.
B: And he never will agree to them, trust me.

The displacement is not obligatory. When the second clause is full, never may occupy its normal place; in this case, never bears the stress.

^okHe has not agreed, and he will never agree.
^okShe is not mine, and she will never be mine.
^okI don't like sushi, and I have never liked sushi.

But when the auxiliary stands alone, with what follows it (the complement and/or the main verb) ellipted, the never must precede the auxiliary.

^okHe has not agreed, and he never will. ... but
^∗ He has not agreed, and he will never.

^okShe is not mine, and she never will be.^† ... but
^∗ She is not mine, and she will never be.

^okI don't like sushi, and I never have. ... but
^∗ I don't like sushi, and I have never.

^∗ marks a usage as unacceptable

^† Note that in clauses where the lexical verb is be acting as a copula (linking verb), the be cannot be ellipted; these are both ungrammatical:

^∗ She is not mine, and she never will.
^∗ She is not mine, and she will never.

But when the lexical verb is be without a complement, in the sense “exist, occur”, it can be ellipted, and the rules I describe above apply:

^okThis must not be, and it never will be.
^okThis must not be, and it will never be.

^okThis must not be, and it never will.
^∗ This must not be, and it will never.

Some cities have a rule requiring that a certain percentage of the budget be used to fund public art.

The clause beginning with "requiring" employs the subjunctive mood, more precisely, the so-called mandative subjunctive:

I require that the budget be used to fund public art.
We asked that it be done yesterday.

Mandative subjunctive uses the "bare infinitive", the basic form of the verb without the particle to.

The mandative (or "present") subjunctive expresses a circumstance that is desired, demanded, recommended, necessary, etc.

If you spot a verb like insist, suggest, demand, prefer, an adjective like necessary, desirable, or a noun like recommendation, necessity, and after (or subordinate to) it, a that-clause, it's a good sign you have a mandative subjunctive.