Variable stiffness technologies help to solve the conflicting requirements of strength, comfort, and safety in soft exoskeletons. Here, we propose a modular variable stiffness strip based on layer jamming as a mechanical solution to constrain users' degrees of freedom and/or to implement wearable anchor points. Equipped with integrated capacitive strain sensors in the longitudinal direction, the strip is 30 mm wide and 3 mm thick and has a modular design that enables its adaptability to different morphologies and force requirements. If negative pressure in the order of tens of KPa is applied, the strip undergoes a stiffness change by a factor of 600, thus ranging between stretchability typical of elastane and inextensibility up to a maximum resisting force of 60 N. The versatility of the strip is shown by integration in an upper body exosuit.