This is a working answer — there will be updates to it (I'll remove this when I think it's done). Throughout this, I use the standard asterisk in front of a statement that is not grammatical.
1. What is a determiner?
A determiner is a word that goes with a noun let's us know which, if any, (out of all of those nouns in the whole of existance), we're referring to. Traditional grammar doesn't consider it a part of speech unto itself but consisting of articles and certain specialized adjectives.1
For example, if we wish to speak of apples, there are many ways to frame the reference:
- an apple one single apple, doesn't matter which
- some apples more than one apple, doesn't matter which ones
- the apple one single apple in particular
- the apples more than one apple in particular
- all apples every single apple
There are also what are known as determiner clauses, that can delimit and specify in similar ways to these single-word determiners.
Depending on which grammarian you ask, there either exists a special determiner called the "zero-determiner" or we simply say that nouns can exist sans determiner:
- Ø apples some amount from two to the entirety of apples in an imparticular, indefinite manner
It is this particular form that interests us here.
2. The Zero Determiner (sustantivos escuetos en español)
In Spanish, pretty much any noun can be made escueto to ascribe it generic qualities. In fact, this generic sense is particular important when adjectifying nouns using de:
- libro de papel
- libro de [ un | el | mucho | poco ] papel
Papel, as a sustantivo escueto, comes to represent a generic material from which the book is made. Attach a determiner to it, and all of sudden, we're not talking generic paper (even if we say un papel, we have defined it to be some particular type of paper, even if unspecified). Even a quantifier like mucho is enough to through us out of something truly generic and start describing the book beyond its mere material.
When used as the object of a verb, a sustantivo escueto can convert the verb from a specific action to express the generic concept of said action:
- Jugaba con mis amigos specific and defined friends of mine
- Jugaba con unos amigos specific, yet undefined, friends of mine
- Jugaba con amigos neither defined, nor specific, could be any number of any friends
In many cases, it may simply be we don't care about the specificity or definitiveness of the object. If I say in English, "I went out with friends last night", who those friends were is completely unimportant, but the idea that I went out with people with whom I have a platonic relationship is. That is what I mean here by the concept of an action.2
3. Restrictions on forming sustantivos escuetos
In general, an uncountable noun can be used sans determiner without problem: compré [la] arena. A countable noun generally needs to be put in the plural to go bare: *compré libro but compré libros.
The lines here can be a bit fuzzy, as there are many nouns that have both countable and uncountable forms.
4. Syntactical restrictions on using sustantivos escuetos
In general, there are no restrictions on using sustantivos escuetos when they are direct objects of a verb or objects of a preposition.
As indirect objects there is no particular grammatical restriction, but as §15.12o of the Gramática notes, it's difficult because “tienden a designar individuos específicos. Aún así, se usan a veces en la interpretación de tipo o prototipo”.
However, in the subject position, as a general (but not definitive) rule, they are not allowed. Compare:
- Los niños compran los libros.
- Los niños compran libros.
- *Niños compran los libros.
- *Niños compran libros.
Technically, the third one there isn't ungrammatical. It just doesn't mean remotely the same thing: los libros are now the subject, somehow managing to purchase children(!).
This is not, however, the source of the restriction (although it certainly doesn't hurt it!). According to the Gramática (§ 15.12a)
La posición más resistente a los grupos nominales escuetos es la de sujeto preverbal, como revela el marcado rechazo de oraciones como *Turistas llegaron a la ciudad. Esta incompatibilidad se debe a que tal posición está generalmente ocupada por segmentos que funcionan como tema o soporte de la predicación (§ 40.1d) por lo que requieren alguna clase de determinación o cuantificación.
5. Exceptions to the subject-case rejection
The general exception to the rule is in passive voice sentences, where the subject (the direct objects from the active sentence) may be escueto if it was in the active as an object:
- Libros fueron comprados por [los] niños
When a verb is conjugated reflexively, it will generally allow (but by no means oblige) an escueto subject in part because the subject is now also the object which as we've mentioned, doesn't require it.
Another sort of general exception is in contrastive situations:
- Agua es lo que necesitamos (y no comida)
- *Agua es necesaria para vivir.
The primary group of verbs that can accept sustantivos escuetos as subjects are called inaccusative verbs. These include verbs like llegar, faltar, existir (for a more exhaustive description of these, go to §41.4 in the Gramática). These verbs tend to describe things as happening, rather than being specific actions with a particular agent, and they can only accept them posposited:
- Existen reglas.
- Nacen animales.
- *Animales nacen.
- *Corren niños
In §15.12k, you can see that when there is a location expressed in the sentence, you can have a posposited determinerless subject with some intransitive verbs (specifically the “pure intransitives”): Allí bailan alumnos but not *Alumnos bailan allí.
In §15.12l, the Gramática states that it's possible to have a determiner-less subject under two conditions: postposited direct object and postposited subject when the direct object has been lexicalized with the verb, or with a thematic direct object (preposited direct object obligating the coappearance of a direct object pronoun). But if you look at them closer, you'll see that I believe they've made a mistake — at least, depending on one's definition of determiner, which does vary from grammarian to grammarian:
- Se dan cita importantes especialistas que pronunciarán una serie de conferencias.
- Muchas de esas historias las han escrito compatriotas vuestros.
In each case, while there is no preposited determiner, we have created specificity either via a determiner clause or just a postposited determiner (vuestros). Get rid of the italic parts, and these sentences sound odd to me. This is basically what they talk about in §15.12b,e, that is, as long as you given the specifying information in some way —before or after the verb— that provides the same function as a determiner (that is, a determiner clause), you can probably omit the determiner in front of the noun. Hence, while normally some of these phrases can be omited without affecting the grammaticality of a sentence, in these examples, they are mandatory:
- Personas de las familias extranjeras son más abiertas.
- *Personas son más abiertas.
- Libros de mi biblioteca son baratos.
6. Moral of the story
When in even the slightest amount of doubt, determine the subject! All of the above exceptions are perfectly grammatical using a determiner (though that may entail a slight change in meaning). On the other hand, removing the determiner when you can't sounds positively awful, and will painfully stick out in otherwise decent Spanish.
1. Some modern grammars, on the other hand, do consider it separate. The Cambridge Grammar of the English Language lists the determinative as a separate word class (part of speech) — for it, determiner is a function rather than a class, but this is a moot distinction for us.
2. Hence in English, aphorisms are so commonly determiner-less: Water is wet (we don't care which water), Girls have cooties (the number of girls and/or cuties, as well as their type and/or specific relation to me is unimportant)
3. That is, the direct object is seen as part of a phrasal verb