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I'm not a native English speaker and I see a sort of striking contradiction in the use of the expression in the passive voice

something can/can not be + past participle

e.g

the problem can not be solved

or

I can't be killed

or

the door can be opened

I know what the English native speakers want to say with this expresion but I see it weird to attribute "can" to an object ; then "can" and the passive voice are contradictory - isn't it like saying :

the door can undergo to be opened

Can is bound to all what relates to ability,action...while the passive voice is bound to the passivity,non action...thus the expression is like

the door is active to be passive

1)"can" and "undergo" does not go together !

2)It's human that can,not objects (such as "doors") or abstract things (such as "problems")

I know ,maybe, I have not well explained my idea - but is this a legacy from an old language or just an habit that became a rule ?

There is no mystery.
In a passive sentence the subject becomes the agent, which is often omitted.

• The problem can't be solved. (by anyone here) = No one here can solve the problem.


• The door can't be opened (by us) = We can't open the door.

The agent is the person or thing that performs the action and is the subject of the active sentence. In most passive sentences, the agent is not mentioned. If it is mentioned, however, it is usually preceded by the preposition by.

Grammaring

"Can" is potentially ambiguous between a permission sense and a possibility sense. "This door can be opened" in the permission sense is "Someone (unspecified) has permission (for that person(s)) to open the door" but in the possibility sense means "It is possible (for someone/thing) to open the door."

In the possibility sense, there is no change of sense when the clause with "open" is passivized: "It is possible for the door to be opened (by someone/thing), which can be expressed using "can": "The door can be opened (by someone/thing)."

In the permission sense, however, passivizing makes for a difficulty. "Someone (unspecified) has permission for the door to be opened (by that person(s))" is not entirely coherent, and it cannot be simplified and rephrased with "can", "The door can be opened", because it implies that "the door" is receiving permission. Doors are not people, so they can't be given permission.

That is an interesting observation you are making. I think you are trying to say that the actual subject of the sentence doesn't appear to be the logical subject, and there is no logical subject in fact. I.e., "The problem cannot be solved" can be paraphrased as "It is not possible for the problem to be solved."

A similar phenomenon in English is with the word seem. E.g., "Thomas seems to be angry." is like saying "It seems that Thomas is angry." This is called "raising" in Linguistics literature.

In passive voice the subject is acted upon by whatsoever in this world. That is to say the receiver of action is made to usurp the subject position. The way we use BE in passive voice is rather, to be true, structured— one of formation of conjugation; it would be wrong to seek a meaning of the use of BE. You should also mark " CAN" does not take an object; it " fine-tunes " the " mood" of the following active verb that takes the object.

Now, YOU CAN SOLVE THE PROBLEM.