How could I give a twist to the story "The Last Leaf" by O. Henry and change the climax?

Of course, the story already ends with two typical O'Henry twists: the leaf Johnsy thinks is real turns out to have been painted, so it is art's illusory qualities, not nature, that saves Johnsy's life. The second twist is that, in painting his masterwork of the leaf to help save Johnsy from pneumonia, Behrman himself dies of the pneumonia he catches while out painting.
It is hard to improve on O'Henry, who was the master of the ironic twist, but there are other ironies we could imagine. What if it turned out, for instance, that Behrman's carefully painted leaf washed away in the rain, and it was a real leaf that was the salvation of Johnsy? That is a very dark ending, as it would mean Behrman's life was thrown away for nothing, but it is another way to imagine the story. It would also be interesting to think that, in painting this last leaf, Behrman managed to atone for some crime from his past. That's much more upbeat than the idea of his leaf washing away! As you let your imagination go, more and more ideas will no doubt occur to you.

The climax of the actual O. Henry story is that Johnsy survives having pneumonia and Behrman dies after painting a leaf on the wall so that Johnsy doesn't see the last leaf fall. If you want to change the climax, you can change either part of the resolution of the story. For example, Johnsy can sadly die after she sees the last leaf fall from the wall. Another ending might involve Behrman surviving instead of perishing from pneumonia. A third potential ending might involve Johnsy surviving and Behrman surviving as well. If you wanted to add a twist to the story, Behrman could become a well-known painter after news of his painting the leaf on the wall begins to spread. People could arrive from miles around to see his masterpiece, and he could achieve the fame and renown he has long sought but has not to date achieved.