Consider these examples:
They are everywhere.
There is food everywhere.
I used sentences like these a lot but lately I realize that everywhere is an adverb. What about those grammar rules that say "using adjective with linking verb" ?
Some “adverbials” can act as adjectives. Locatives in particular—expressions which designate a location in time or space—can modify a nominal as well as an “action”, and thus may be properly employed as the complement of a linking verb:
Elizabeth is on the left.
We are ahead of schedule.
The keys could be anywhere.
Traditional grammarians sometimes try to get around this awkward fact by claiming that these “adverbials” modify the linking verb; but this is clearly wrong, since a) this leaves the verb without a complement, and b) the same constituents can be employed in contexts where they clearly modify nominals:
The ball on the left is bigger than the ball on the right.
We’d be grateful if anybody ahead of schedule on their own project could lend a hand getting ours out the door.
Anybody anywhere can do this.
An adverb modifies a verb or an adjective.
You are correct that in sentences with a linking verb, the predicate modifier is usually an adjective. That is because the modifier is refering to the subject, which is a noun or pronoun.
However, in a few senteces using verb that may be considered linking, the predicate modifier is actually modifying the verb. In the exaples you give, everywhere modifies is and are.
They are [they exist]. Where are they [where do they exist]? Everywhere.
The rule "After to be follows an adjective" is simply formulated wrong.
If you read texts carefully you will see that the rule "After to be follows an adjectve" is simply wrong.
You have to reformulate your rule: one of the sentence types with to be is to be + adjective. But there are also sentence types such as to be + noun or + adverbials/adverbs.
When you ask when was it the answers can be - That was after the war/ in1963/ on last Monday/recently/yesterday. Here you have when-indications after to be, and no adjectives.
If you clarify the question, it'll be better. What you want to know? If you firmly believe that an adverb should not be used after a linking verb, I'm afraid, this is incorrect.
I'm not aware of the rule that denies a linking verb not taking an adverb after it. The simplest example is...
She is here! Here, is is a linking verb and here is an adjective. It's simple and clear.
Yes, we have rules for adverbial positioning and I think it'll be helpful.
The adverbs of manner (how), place (where -this is your case), and time (when) generally go in end position.
There is food everywhere (-place).; She brushed her hair slowly (-manner).
Another thing, Swan's book describes that in such cases, here and there begins the sentences. So again,
Everywhere there's foodThere's food everywhere.
It rocks! When we generally go by rules, we have to accept some exceptions to them. Using adverbial complements for linking verbs is yet another example for this exception. Normally it goes by written rules. But, when we ask question like 'where?', we have no other option than giving an adverb as answer.
For example, if anyone asks, 'Where is she?', you cannot answer, 'She is pretty' or 'She is a student'. Here, you have to tell where she is. To express her location, you have to use an adverb or adverbials (as we all know, adverbs only can be the answer for such questions). Hence, the answer could be 'She is in New Delhi' or 'She is on the upstairs' or ' She is in the next room' and so on.
I hope it's clear.
It is actually pretty simple. Adverbs of time and place CAN follow 'be' verbs. I don't view these be verbs as actually being linking verbs in these situations. However, it does indicate a 'state of being' in the specific sense of time or place. In your example, "They are everywhere.", and in many possible examples, we see adverbs after a 'be' verb. I believe that be verbs are usually linking verbs. There is a lot of misinformation on the web. Then someone wants to make a new grammar website and does their research on the Web and just propogates an unclear statement. The linking verbs that are NOT "be" cannot have an adverb after them. (seem, feels, tastes, become, etc.) In the, generally accepted list of English sentence patterns we will see that the first one is the example we are talking about. This is widely accepted.