There is a phrase из лесу, meaning "from the forest". Also, you may say "из леса", which seems to me much more sensible. But I'm wondering if лесу really is some realisation of the genitive case, singular. If so, it ought to be possible to:
Modify it with an adjective. For example: Он ушел из глубокого лесу.
Use it wherever genitive is called for. For example: Он из лесу. (meaning, "he's from the forest", of an animal, a piece of wood, or whatever)
Without preposition из. For example, состоянье лесу, for "the condition of the forest".
Which of my examples are grammatical? Or are none of them, except "из лесу"?
лесу— is locative form. In modern russian it's considered obsolete. You may use it, but it will sound quite archaic. – user28434 May 26 '20 at 09:35