Paper, an inexpensive material with natural biocompatibility, non‐toxicity, and biodegradability, allows for affordable and cost‐effective substrates for unconventional advanced electronics, often called papertronics. On the other hand, polymeric elastomers have shown to be an excellent success for substrates of soft bioelectronics, providing stretchability in skin wearable technology for continuous sensing applications. Although both materials hold their unique advantageous characteristics, merging both material properties into a single electronic substrate reimagines paper‐based bioelectronics for wearable and patchable applications in biosensing, energy generation and storage, soft actuators, and more. Here, a breathable, light‐weighted, biocompatible engineered stretchable paper is reported via coaxial nonwoven microfibers for unconventional bioelectronic substrates. The stretchable papers allow intimate bioconformability without adhesive through coaxial electrospinning of a cellulose acetate polymer (sheath) and a silicone elastomer (core). The fabricated cellulose‐silicone fibers exhibit a greater percent strain than commercially available paper while retaining hydrophilicity, biocompatibility, combustibility, disposable, and other natural characteristics of paper. Moreover, the nonwoven stretchable cellulose‐silicone fibrous mat can adapt conventional printing and fabrication process for paper‐based electronics, an essential aspect of advanced bioelectronic manufacturing.