Technologies that are able to handle microvolumes of liquids, such as microfluidics and liquid marbles, are attractive for applications that include miniaturized biological and chemical reactors, sensors, microactuators, and drug delivery systems. Inspired from natural fibrous envelopes, here, we present an innovative approach for liquid encapsulation and manipulation using electrospun nanofibers. We demonstrated the realization of non-wetting soft solids consisting of a liquid core wrapped in a hydrophobic fibrillar cloak of a fluoroacrylic copolymer and cellulose acetate. By properly controlling the wetting and mechanical properties of the fibers, we created final architectures with tunable mechanical robustness that were stable on a wide range of substrates (from paper to glass) and floated on liquid surfaces. Remarkably, the realized fiber-coated drops endured vortex mixing in a continuous oil phase at high stirring speed without bursting or water losses, favoring mixing processes inside the entrapped liquid volume. Moreover, the produced cloak can be easily functionalized by incorporating functional particles, active molecules, or drugs inside the nanofibers.