Articles – Does the Adjective ‘Same’ Always Require ‘The’?

Not a clarification, not optional

When you omit an article where it is expected, a listener thinks that you mean something different—otherwise you would have included the article. So, omitting it is not optional.

For example, if you say:

I adopted two cats. The cats, long ago, were worshiped as gods.

The second sentence means that the two cats you adopted were once worshiped as gods. A listener will understand long ago to mean within the lifetime of your two cats.

Removing the article changes the meaning:

I adopted two cats. Cats, long ago, were worshiped as gods.

Now, the second cats doesn't refer to the two cats you adopted. It refers to cats in general. A listener will understand long ago to mean probably thousands of years ago.

So, the definite article is not there to optionally clarify the meaning. It's there to maintain the thread of reference to the same cats. Without it, the thread of reference is broken, and cats must now refer to something else.

A listener can often infer your meaning but the grammar is still wrong

In your examples:

I was walking with some friends. Friends were very funny.

We made a stop. After making a stop, we moved on.

it's hard to tell what else friends and stop could refer to other than the friends and the stop mentioned in the first sentence. So, a listener will probably figure out your intended meaning, but the listener will also think that you made a mistake—or that perhaps he did not understand you right.

In the second example, a listener might wonder if you are talking about two stops or just one, since the indefinite article here would normally introduce a new instance and you would have said the definite article if you meant a previous instance. A listener can hear the second example as grammatical, though, by understanding you to mean make a stop as an indivisible concept, as if you had said “We stopped. After stopping, we moved on.”

It’s normal for a noun to be preceded by an article

It might help to think of “the noun” and “a noun” as the normal ways that a noun appears in sentences. You must have a special reason to omit the article. There are many of these special reasons, of course, and they occur frequently: talking about the kind of thing abstractly, a modifier like this or any or every which makes the article redundant, various kinds of nouns that don't usually take articles, etc. But if you want to think like a native speaker, then when you learn a noun, you should think of it with an article: “a friend”, “a cat”, “the steering wheel”, etc.

Notice that when native speakers define a word or concept, they usually precede it with the article that illustrates its normal, typical usage when it first appears in discourse: “a cat is a small, furry animal often kept as a pet”, “the stomach is the organ that holds food just after you eat it”. Notice that it’s not “a stomach…” Also, definitions usually indicate when a noun is not normally preceded by an article: “digestion is the process of absorbing food into the body.” (Nobody says “a digestion”.)

As an added bonus, learning every noun with its usual article also gets you accustomed to the rhythm of English: “da DUM da DUM da da DUM…” Speech without these little "up beats" leading to stressed beats sounds strange and a little hard to understand.

This answer addresses the two questions at the bottom of the body of your question, but only tentatively addresses the question in your title.

The grammatical construct where the article is missing appears to be called the zero article. There is also a book written about the zero article.

One might have thought that zero articles are used when the noun is inherently unique, since there is no need then for an article to distinguish any one of many from a specific one of many. However, English is inconsistent here. One example that has come up in a similar discussion is The Eiffel Tower. Another example (from the book, IIRC) is The Baltic Sea. In both cases, the noun is unique but the definite article is part of its name.

One suggestion is that we always use the zero article with names. In examples such as The Eiffel Tower and The Baltic Sea, the word The is considered to be part of the name rather than a separate article. Street names are similar. For example, "Where is Main Street?" has no article but "Where is The Strand?" does because The is part of the name The Strand. Note that this doesn't cover all cases since "I can design an Eiffel Tower" and "I can pave a Strand" are arguably acceptable. In many cases, though, this 'rule' holds.

In the case of your question, Room 401 is the name of the location, but the location is not so grand as to warrant having "The" as part of its name. The definite article is therefore not used before Room 401 in the sentence in your question's title.