There is no such thing as "a salt that makes ice unable to refreeze". Well, sort of depending of the conditions.
What happens is that salts added to pure water ice form a solution (of the salt in the melt water) that has a much lower point of freezing that pure water ice.
This is known as the freezing-point depression (Wiki for the basics).
For example, adding common salt (sodium chloride) to pure water ice will depress the freezing point of water to about -21°C, so ice will melt until the solution will reach this temperature. Then, you'll have an equilibrium of -21°C salt water and -21°C solid ice.
If kept at the freezing temperature of pure water, the salt water will never re-freeze on its own.
If you take this salt water (now at -21°C) and lower even more its temperature, it will then freeze, forming salt-water ice.
Other salts (like sodium acetate used in airports, for example) will give you different temperatures, but all of them will re-freeze if the temperature is lowered below some definite temperature dependent on the salt and concentration.