Industrial manipulators offer reach and precision but can damage nearby structures in confined spaces. Soft robots provide compliant contact but typically have limited reach. Rigid-soft systems combine their advantages, although they often require dedicated actuation and control hardware. We propose actuating a passive tendon-driven soft extension through manipulator joint motion. As the robot moves, the exterior spans of tendons anchored to upstream links change, altering tendon tension and deforming the extension. Inspection through narrow apertures, for example, constrains the motion of the end effector (EE). We develop a controller that regulates the soft tip while preserving such EE constraints. A differential model separates rigid transport from soft deformation, combining analytic arm and tendon kinematics with a locally identified span-to-deformation map. We also derive a local upper bound on the number of independent deformation directions transmitted by the tendons under the EE constraint, and conditions for the exponential convergence of the tip error. A quadratic program with control barrier functions imposes obstacle clearance, fulcrum limits, and model-validity conditions. Simulations and real experiments show tip and shape regulation under free, position-constrained, and fulcrum-constrained EE motion.

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