If the yucca moth goes extinct, the most likely outcome for the yucca plant is that humans would have to engineer a way to pollinate the plant. This is because the yucca and the moth have a specialized mutualistic relationship where the moth is the primary pollinator of the yucca plant. Without the yucca moth, the plant would not have its natural means of reproduction.
While it is possible that some other pollinator could adapt to take over the role of the yucca moth or that the plant might evolve a new method of pollination over a long time, such processes typically require a longer timeframe and are not guaranteed. The immediate threat posed by the extinction of the pollinator most likely points to human intervention being necessary to preserve the yucca plant.