It may depend on the exact circumstances. More than a year ago, before AA and US began their merger, I had an AA award ticket MUC-DUS-JFK-DCA, with the first two flights on AB and the last flight on AA. Because of weather problems in Washington, AA cancelled the JFK-DCA flight and rebooked me on DL. When DL cancelled its flight, they rebooked me on US LGA-DCA. I had to pay for the trip from JFK to LGA, but I mad it home that evening, and US gave me UA mileage for the last segment.