Webb made money swimming. He lost a lot doing one thing and another (I am shady on the details because I don't know enough about Captain Webb either, though I know more about him than you). He did races in the Atlantic off America and earned $1,000 by floating for 128 hours in a tank of water at the Boston Agricultural Show.
On July 24, 1883, he went swimming under Niagara (hoping to make $12,000). According to a friend quoted in Haunts of the Black Masseur: The Swimmer as Hero, by Charles Sprawson:
We discussed Niagara. "Don't go," I said. "From what I hear, you will never come out alive." "Don't care," was the reply. "I want money and I must have it." As we stood face to face, I compared the fine handsome sailor, who first spoke to me about swimming, with the broken-spirited and terribly altered appearance of the man who courted death in the whirlpool rapids. His object was not suicide, but money and imperishable fame.
Webb looked around, said 'If I die, they will do something for my wife,' jumped in and died.