When talking about soft robots, softness is considered the most important feature, which brings dexterity and safety in interactive tasks with humans and environments. Such softness sometimes limits the real application of soft robots because load capability and rigidity are widely needed on many occasions. Often the inspiration for soft robots, soft animals such as octopus and sea cucumbers still preserve the ability to turn rigid when needed, and, more importantly, they can rapidly turn rigid at any deformed states. Intrigued by these capabilities, differently from existing stiffening technologies that do not adapt to soft robots' variety of morphological changes, we explored a new approach to create a flexible layer that can easily stiffen soft robots without affecting their original flexibility. We built an extensible chain of particles with a peculiar geometry, which can jam and stiffen. We enclosed it in a flexible membrane so that we can stiffen the structure by removing air. The overall structure is flexible enough and can withstand large elongation. So, it can be used around a soft robot arm for stiffening it in different deformed states. Experimental results show that such a stiffening layer does not affect the flexible motion of the soft robot, the stiffening function works even under the robot's 90% elongation state, and the stiffness can be increased by 15 times. By adopting the stiffening layer and different end effectors, we show that an assistive soft robot can simultaneously have the flexibility to collect food and the rigidity to hold it and help in feeding a participant. The results from this work may provide new design and application insights into the creation of soft robots with both flexible and rigid features.