At the end of the movie, that sketch of Caesar Suzzi that arrived late from the fax machine—what warnings or messages do you think were written on it besides the portrait?

Ha, that question hits the nail on the head! The ending of The Usual Suspects is absolutely a classic in film history, and that piece of paper from the fax machine is the "knockout punch" for both the audience and Agent Kujan.

Although the film doesn't give the paper a full, clear close-up, based on the plot and common sense, this fax – dictated by the Hungarian survivor and drawn by the police sketch artist – likely contained the following information alongside the familiar face of "Verbal" Kint:

1. Core Content: Witness Description and Warning

This is the most crucial part. This paper isn't just a sketch; it's an official police record from another witness. You can imagine it containing something like this in English:

"Subject identified as 'Keyser Söze'."
"Witness was extremely agitated. Kept repeating the name 'Söze'."
"Described the subject as 'the Devil himself'. Extremely dangerous. Use extreme caution."
"He is not Turkish. He speaks fluent Hungarian with a German accent." – This point might also be included, shattering the myth of Söze's Turkish identity.

In short, what's written on this paper is the terrified warning delivered with the survivor's last strength from his hospital bed – burned beyond recognition – to the police. He didn't just sketch Söze's face; he described his terror in words.

2. Official Information

As an official police document, it would also contain standard formatting, such as:

From: Port of Los Angeles Police Department or Cooperating Hospital Police Liaison
To: Agent Dave Kujan or his U.S. Customs Service Office
RE: San Pedro Pier Shooting/Explosion Survivor Testimony
Date and Time

The Fax's True "Dramatic Function"

What's more interesting is that the fax's role in the film is not actually to reveal the truth to Agent Kujan.

You see, Kujan's realization comes when he stares at the bulletin board in his office and connects all the keywords from "Verbal" Kint's story (Redfoot, Kobayashi, the Guatemalan coffee cup...) with the clues pinned there.

Meanwhile, that fax machine had been whirring and clicking away slowly in the background the entire time.

For the audience, we watch the truth (that face) being printed out line by line while the protagonist Kujan remains oblivious, cranking the tension to the max.
For Kujan, just as he has his epiphany and his coffee cup clatters to the floor and shatters, the fax finishes printing. This paper flutters to the ground, picked up by his colleague, becoming the straw that broke the camel's back. It serves as a merciless taunt, telling him in black and white: You've been played, and the evidence was sent to you all along, you just didn't see it.

So, while what is written on the paper matters, the very act of its "belated arrival" is the director's most brilliant design. It perfectly illustrates that classic line:

"The greatest trick the Devil ever pulled was convincing the world he didn't exist."

And by the time people finally get his picture, he has already "limped away" into the crowd.