A binary ionic compound contains just two elements, a metal and a non-metal, for example lead bromide or potassium iodide. Solid lead bromide does not conduct because its ions cannot move. When it is molten the ions are free, so it conducts and can be electrolysed.
A molten compound contains no water, so the only ions present are the two from the compound. This makes prediction simple. The positive metal ion goes to the cathode and forms the metal. The negative non-metal ion goes to the anode and forms the non-metal. No hydrogen forms because there is no water.
Name the products from the compound's name. Chloride gives chlorine, bromide gives bromine, iodide gives iodine and oxide gives oxygen. So molten sodium chloride gives sodium and chlorine, molten lead bromide gives lead and bromine, molten potassium iodide gives potassium and iodine, and molten aluminium oxide gives aluminium and oxygen.