I don't know if this is the issue, but sometimes when the print head crosses a perimeter, it can pick up a strand of deposited filament and move it. Slic3r has an "avoid crossing perimeters" setting to avoid this.
Still, it shouldn't happen.
When does it happen? If it's the nozzle dragging something loose, that's a different problem than if it happens when the layer starts. Keep watch of when it happens, and that should give you a hint as to the solution.
If it happens when the nozzle makes non-print moves, and some plastic oozes from the nozzle, that's something to look at retraction. If it happens when the nozzle moves away from or crosses the perimeter line, then that's a different issue.
MBot3D Printer
MakerBot clone Kit from Amazon
Added heated bed.
Leadscrew self-built printer (in progress)
Duet Wifi, Precision Piezo parts