It depends. Yes, the stringers need to be supported along their length, but they can span a few feet too, depending on 1) the width of the stairs, 2) the number of stringers, and 3) size of riser board.
1) The wider the stair the more load will be transferred to the stringers.
2) More stringers can span further because they'll be carrying less load.
3) Most stairs have the stringers, on the edge, nailed to the walls that run parallel to the stair. Then, the riser board is fastened to each stringer. So, the interior stringers are actually supported by the riser board that spans from side-to-side. The thicker the rider board and the shorter distance the riser board spans, then the more load the stringer can carry and the longer it can span.