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Legged robots constructed from soft materials are commonly claimed to demonstrate safer, more robust environmental interactions than their rigid counterparts. However, this motivating feature of soft robots requires more rigorous development for comparison to rigid locomotion. This article presents a soft legged robot platform, Horton, and a feedback control system with safety guarantees on some aspects of its operation. The robot is constructed using a series of soft limbs, actuated by thermal shape memory alloy (SMA) wire muscles, with sensors for its position and its actuator temperatures. A supervisory control scheme maintains safe actuator states during the operation of a separate controller for the robot's pose. Experiments demonstrate that Horton can lift its leg and maintain a balancing stance, a precursor to locomotion. The supervisor is verified in hardware via a human interaction test during balancing, keeping all SMA muscles below a temperature threshold. This work represents the first demonstration of a safety-verified feedback system on any soft legged robot.