What would happen during a tug of war between sodium and chlorine over each others electrons? why?

The number of valence electron in sodium is 1 and that in chlorine are 7. In order to complete the octet (8 electrons in outermost shell) sodium can give its valence electron to an atom with more electronegativity. Here, chlorine is more electronegative than sodium, due to 7 valence electrons it required one more electron to complete its octet.

Therefore, chlorine can take 1 valence electron of sodium to form ionic bond. In the ionic compound so formed, both sodium and chlorine have complete octets. In aqueous solution they exist as and ions, the positive charge on sodium indicates that it donates its one electron and negative charge on chlorine indicates that it accepts an electron.

All this happen due to difference in electronegativity of sodium and chlorine (chlorine is more electronegative than sodium).