In "A Worn Path," Welty leaves it ambiguous whether or not the grandson is dead. The story is told from the point of view of the grandmother, Phoenix, who succeeds as an old woman in making the perilous trip through the woods on foot to town to get medicine for her grandson. She is convinced he is alive and, when she comes up with ten cents after getting the medicine, says she is going to buy him a toy windmill as a Christmas gift. She also tells the nurse who questions her that he's not dead, but "just the same."
However, there is strong evidence that the boy may be dead. The nurse says that he swallowed the lye "two—three years ago." It seems unlikely, given that children grow fast and bodies heal or change, that he would be "just the same," as Phoenix contends, if he were alive. There are also hints that Phoenix sees the boy's ghost as she journeys. We also know that she is forgetful, for she forgets when she arrives in town why she has come. She also refuses to say how old the boy is now. He seems frozen in time to her, as a dead child would.
Welty herself discusses this question in a 1978 New York Times article. She leaves ambiguous whether the boy is alive, saying only that the grandmother believes he is and that it is up to the reader to decide. As she points out, the important point is that Phoenix makes the journey.