We propose a method for deciding an avoidable stop position for a vehicle to not disturb the surrounding traffic. A vehicle needs to pull over and make an autonomous emergency stop when a driver has a seizure and loses consciousness. To develop such an autonomous stop system on a narrow road, considering the surrounding vehicles and not hindering traffic are imperative to rescue a patient. We present an approach based on predicting the paths of other vehicles to avoid the ego-vehicle, a load index of a following vehicle driver for predicted paths, and an index that shows the interference between the paths of the following and oncoming vehicle. The path prediction is computed by applying a lattice path planner comprising the vehicle's position, posture, and path curvature. The load index of the following vehicle is calculated with respect to the cumulative curvature of the predicted path. The interference index of the following and oncoming vehicles is estimated by evaluating the area that both vehicles pass to avoid the ego-vehicle. The simulation results showed the ego-vehicle had to pull over by 1.5 m over the road shoulder and 1.0 m ahead of a parked vehicle on the opposite lane.