In general, there are some inorganic salts (containing transition metals) which have significant solubility in solvents such as ethers (e.g.THF) while they preserve their salty nature.
The salts of the first 3 Groups of the Periodic Table (including Na) have high lattice energies which cannot be overcome by the solvation energies provided by moderately polar aprotic solvents such as THF. If few Na ions are separated from their salts, then they will just undergo strong complexation with THF "a process that cannot be categorized as dissolution, at all".