As a noun: The headstrong don't easily give up.
As an adjective: The headstrong youth.
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While there are lot of Adj/N pairs in English, your example seems to be of the specific type 'Nominal Adjectives' (e.g. 'the meek', 'the poor').
I wouldn't say they're nouns in their own right; you can't clearly swap them into other sentences ('A headstrong doesn't give up' or 'I'm looking for a headstrong'.)
Even when it is true that there are identical N/Adj pairs, they're often nouns used as adjectives ('ham' in 'ham sandwich'); that is, 'noun adjuncts'.
In addition, there's a very common practice in English (very popular in recent marketing) of what you could call 'zero-derived deadjectival nouns': 'Think different', 'Eat fresh', etc. Less obviously marketing-based examples are things like 'I was attacked by some toughs'.
Finally, English has a number of non-homophonous homonym N/Adj pairs: e.g. 'concrete'/'concrete'. However, even when such a pair is homophonous, it would be the same: a homonym/homophone pair of two distinct words.
The best term to denote headstrong when it functions like a noun is nominal. The term nominal is broader than the the term noun. Any word that functions as the head of a noun phrase is a nominal. Thus if the head of a noun phrase looks like an adjective (e.g. the good, the helpful, the first, the best, etc.), then one can use the term "nominal" to denote it.
The terminology in this area is of course not used consistently. There is confusion about the distinction between nouns, nominals, and substantives. For most of us, the noun concept is relatively clear. The term nominal is less clear, but my understanding of it is that it is a broader concept, encompassing nouns, pronouns, and any other word that functions as the head of a noun phrase. The term substantive is older and has fallen out of use. It seems to have been more prominent in the grammars of European languages. It denoted a noun in the narrow sense (not including pronouns and adjectives used as nouns).
The class of adjectives that can be nominals if they are plural and introduced by the is large, e.g. the old, the fat, the skinny, the friendly, the robust, etc. But there may be an animacy requirement on the adjectives that are used in this way. It doesn't seem to work for adjectives that modify inanimate objects, e.g. *the wide, *the red, *the rough, *the smooth, etc.
I've gotten around the problem of inventing a new term (and kind of word) as follows.
The issue of adjectives (or articles, for that matter) functioning alone as complete noun phrases came up in the context of a computational dependency grammar for German. Canonical dependency grammar takes the noun to be the
governor of the noun phrase, and the adjective to depend on it:
["don't give up" ["youth" ["the"] ["headstrong"]] ["easily"]]
if you will.
In German, much inflection is carried by the adjective, even more when it comes alone ("strong" inflectional paradigm as opposed to "weak" paradigm when an article is present). This, in connection with the fact that adjectives precede nouns in German, lead me to the idea that the adjective (and the article) "project" a noun to follow. If the noun does not show up, an empty "shell" (lexically empty noun) is left in the syntax tree.
If this analysis can be applied to English as well, you don't need a special Adj/N class, since (a subclass of) adjectives just simply do project nouns. Well, maybe you need a name for this subclass of adjectives which do that. German adjectives do that across the board.