Co-electrospinning has demonstrated that polymer solutions below the entanglement concentration can be made into fibers as an encapsulated core in an electrospinnable sheath solution containing a carrier/template polymer. The carrier polymer may require removal at a later stage. This work shows for the first time that without increasing the polymer concentration/molecular weight or needing a template polymer, simply infusing a liquid in the core nozzle can cause the sheath polymer solution (viscosity <20 mPa s) to electrospin instead of electrospray in a coaxial electrified jet. Different from coelectrospinning, the core liquid can be a common solvent such as water and does not require a readily electrospinnable carrier polymer. The process was not limited to one core liquid system; infusing solvents and nonsolvents with different properties in the core generated either beaded fibers or continuous fibers from the sheath solution. The process of fiber formation instead of particle breakup was attributed to the relaxation time of the elastic polymer sheath solution becoming longer than the growth rate of the Rayleigh instability in the compound jet upon the infusion of a second solvent in the core. Key parameters of the process included high surface tension of the core liquid (e.g., water and glycerol), high interfacial tension between the core and the sheath liquids, and electrohydrodynamic operating parameters such as flow rate and applied voltage. Given that charge was transferred from the sheath solution to the core liquid, differences in the dielectric constant and electrical conductivity of the core liquids showed little influence on the process. Fibers also formed irrespective of the miscibility and solubility of the solvent, though in the case of a nonsolvent, a lower miscibility was desirable to minimize polymer precipitation at the coresheath interface. The process was investigated using poly(lactide-co-glycolide) as a model system, with polycaprolactone and polymethylsilsesquioxane systems presented as two additional examples. This work documents new roles of solvents in coaxial electrohydrodynamic processes and presents a useful method to obtain micro- and nanofibers from low-viscosity solutions without using a template polymer.