In Bernard Malamud's "The Magic Barrel," I don't see Pinye Salzman as an allegorical figure. Leo Finkle is something of a Christ-like figure, sacrificing himself for the redemption of the "fallen" Stella, however, Salzman's story does not offer this kind of association.

...a caricature is a description of a person using exaggeration of some characteristics...

I see Salzman as a mystical figure. If a caricature, it may well have to do with Salzman's similarity to a fairy godmother. For this to be the case, the reader must recognized how the story begins, and it may sound familiar in style:

Not long ago there lived...

This is particularly similar to "Once upon a time..." The opening introduces a story that could take place anywhere at any time. Leo is much like a "reversed" Cinderella-like figure, not living among the ashes, but residing in...

...a small, almost meager room...

Salzman's magical talents are immediately presented...

The matchmaker appeared one night out of the the dark fourth-floor hallway...

He does not have a black hat—as would a magician—from which he draws all kinds of amazing items, but instead he comes...

...grasping a black, strapped portfolio that had been worn thin with use.

Salzman is less "fairy godmother" and more "Bilbo Baggins" (from Lord of the Rings):

...[he] was wearing an old hat, and an overcoat too short and tight for him...[with]...mild blue eyes.

Michael Ferber in his book, A Dictionary of Literary Symbols, notes...

...blue is traditionally the color of heaven, of hope, of constancy,of purity, of truth...

 

Is Salzman an unlikely angel?

Salzman removes from his bag a stack of "much-handled cards." In mystical circles, tarot cards are used to divine or tell the future. Ironically (or perhaps not), Salzman cannot find Leo's future in the cards.

The next night, Pinye "appears"...

Almost at once there came a knock on the door...

The matchmaker has appeared magically once more out of the dark. For food, he has a hard roll and a small fish: these are found in the Bible's story of the loaves and fishes—a miraculous account.

When Leo goes to the park to meet Lily, he imagines Pinye close by...

...as he danced his invisible way before them.

After Leo sees the picture of Stella that Pinye mistakenly leaves behind, Leo searches for the man, noting (almost as if by magic) that...

...just when he needed [him] he was nowhere to be found.

At Pinye's apartment we discover more "magic." His wife says his office is "in the air." Begging to find him, the wife "predicts:"

Go home. He will find you.

And when Leo gets home, Salzman is there before him! Leo says he wants to meet the girl in the picture—it is Salzman's daughter, Stella. "Stella" means "star," and like the Magi, Stella will lead Leo to his destiny.

Meeting him later, Salzman looked...

...transparent to the point of vanishing.

Salzman believes his daughter is lost to him for her "sins." Leo's words become magical:

"Perhaps I can be of service."

And...

Leaving the cafeteria, [Leo] was, however, afflicted by a tormenting suspicion that Salzman had planned it all to happen this way.

This also alludes to Salzman's magical "gifts." Seeing each other, hope transforms Leo and Stella into people who are changed—made better by the presence of another. This story's end is very much like...

...and they lived happily ever after.

Salzman, for this modern fairytale, is a present-day "fairy god...father"—of sorts.