The wave exits the slits and creates wave interference. As the particle exits a slit the direction it travels is altered by the wave interference. If you strongly detect the particle exiting a single slit it destroys the cohesion between the particle and its associated wave and the particle continues on the trajectory it was traveling.
This is what I think is occurring in a so called "delayed choice quantum eraser experiment".
When the red and blue paths are combined the waves traveling both paths create wave interference which causes the particle to create an interference pattern when detected at D1 and D2. There are no interference patterns at D3 and D4 because there is only the single path to the detector so the particle's associated pilot wave has nothing to interfere with.