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Your conjecture is invalid.

Follow takes an object and an optional locative complement designating the destination or path of movement. But it never has a causative sense: the subject does not cause the object to move.

I don't know what you mean by the second sentence, it makes no sense to me. The sentence you are asking about means: a man walks into the store and is followed by a dog. The dog is walking behind the man.

You are correct that your second sentence "sounds very weird". That is because it makes no sense. It seems to suggest that the man somehow got into the store (was allowed to enter) by "the following of a dog" (because he was followed by a dog), which is just plain crazy, unless the shop only allows humans to enter if a dog goes in after them. Maybe you mean "the man went into the store, followed by a dog". We can use "follow" a number of ways: e.g. to literally move along behind someone or something, or to happen after something else, or to sympathise with and admire (of a leader).

Follow

There are verbs that describe an action of a subject causing an object to enter into something:

I forced a square peg into a round hole.



The students moved their possessions into the dormitory.



The board of directors forced the company president into retirement.



The general sent two divisions into the valley.



The mermaids lured sailors into the ocean.



The artists fastened the painting into its frame.



He poked his head into the room.



She pushed him into the water.



You have painted yourself into a corner.



The child cajoled her parents into buying candy.

Some of those meanings of "into" are more abstract than others, but in all cases the verb is understood as causing the thing described in the "into" phrase.

But plenty of verbs do not have this construction.
For example, it is not possible for me to stand myself into unconsciousness, even if I cause myself to fall unconscious by standing in a bad posture for a long time.
I cannot know a book into a library, even if I am responsible for purchasing books for the library and knowing the book caused me to buy it.

Perhaps the man went into the store in hopes of getting away from the dog that was following him, and therefore the dog caused the man to enter the store by following him. But that fact is not a meaning of the sentence, "The dog followed the man into the store." We do not use the construction followed into to indicate causation.

No, the second meaning does not work. The word follow cannot have that meaning.

For contrast, let's look at a different sentence:

A dog chased the man into the store.

This sentence can have two different interpretations:

1. The man caused the dog to enter the store. (The man chose to run into the store, and the dog ran in behind him.)




2. The dog caused the man to enter the store. (The man was running to get away from the dog, and the path away from the dog led into the store.)

Why can this sentence have more than one interpretation? Because the word chase has more than one meaning, and the sentence does not make it absolutely clear which meaning should apply.

chase - verb (1)

transitive verb

1 :

  a : to follow rapidly : PURSUE

    // a dog chasing a rabbit

...

4 : to cause to depart or flee : DRIVE

  // chase the dog out of the garden

...

(https://www.merriam-webster.com/dictionary/chase)

The first interpretation uses definition 1a. The second interpretation uses definition 4.

For the purposes of our discussion, definition 4 is the more interesting definition. This definition describes a particular kind of relationship between the subject of the verb (dog) and the object of the verb (man), where the action of the subject is causing a certain behavior in the object. (That behavior is "running away".) In short, definition 4 is the only reason we can say that the dog caused the man to do something. If the word chase did not have definition 4, then we could not interpret the sentence that way.

Now, if we look at the definitions for the word follow in the dictionary, do we see any definitions similar to chase's definition 4? That is, do we see a definition where the action of the subject is causing a certain behavior in the object? No, we do not. There is no definition of follow that describes a situation where the dog is causing the man to enter the store.

As others have said, your second interpretation is incorrect. You may, however, have been thinking of a similar phrasing that would be correct, although still unusual.

The dog-following man entered the store.

This makes sense and would be inline with your second interpretation. However, it's kind of hard to come up with a situation where I would actually use it. Maybe in a story about a man who saw a stray dog and decided to follow it to see where it went?

Campbells Chunky Soup once ran an advertisement which stated:

The soup that eats like a meal.

This is a similar structure to what you've pointed out. It does not appear in ELL search results, but here is a link to another forum: https://forum.wordreference.com/threads/soup-that-eats-like-a-meal.2557239/

For reference, I'll copy some examples from there, to here.

For ex., "I load the gun" but also "This gun loads easily"; "I drive the truck" but also "This truck drives like a car".

I think this is similar because your sentence "A dog followed the man into the store" can be reworded as "The man was followed by the dog", where "followed" can take either meaning.