His escape was discovered, but not the way of it
No one thought that Corwin managed to escape via the painting. Why?
- Only Dworkin knows how to create Trumps. No one has seen him for quite a while and he is considered dead. And even if he was alive, what would he do in the Corwnin's cell?
- The Trumps are made as cards and each is a little masterpiece. The drawings on the walls are crude in comparison, made using spoon on the wall. Yes, Dworkin has signed them with his name, but that doesn't mean anything - it is like if someone would create a spray painted graffiti on the wall and sign it "Rembrandt"
- Corwin has been blinded and everyone (him included) believe that it was a permanent disability. While the drawings might suggest otherwise, there are blind painters and sculptors, so the existence of those etchings doesn't prove that he has regained his sight. Why is that important? Because blind people cannot travel through Shadows!
So whoever found the empty cell (probably indeed about week later) came to the conclusion that Corwin had outside help (there is even proof in the form of burned matches), that he left via the door and that he is hiding somewhere in Shadows. No one thought that he escaped via the Trump on the wall and that he would be still in Amber.
Even later, Corwin doesn't admit to the way he'd escaped:
"And of your escape?" he [Benedict] asked. "How did you manage that?"
"I had help, of course," I admitted, "in getting out of the cell. Once out -- Well, there are still a few passages of which Eric is unaware."
"I like to think so," he said. Then, "I understand you left the partly whittled cell door locked behind
you, had set fire to your bedding, and had drawn pictures on the wall."
"Yes," I said. "Prolonged confinement does something to a man's mind. At least, it did to mine. There
are long periods during which I know I was irrational.
Also, it seems that they gave up the search after a while, believing that Corwin is dead:
We looked for you. Did you know that, Corwin?" he asked. "Brand searched for you in many
shadows, as did Gerard. You guessed correctly as to what Eric said after your disappearance that day.
We were inclined to look farther than his word, however. We tried your Trump repeatedly, but there
was no response. It must be that brain damage can block it. That is interesting. Your failure to respond to
the Trump led us to believe you had died