* Electrolysis is a process that uses an electric current to drive a non-spontaneous chemical reaction.

* Brine is a concentrated solution of salt (NaCl) in water. Electrolysis of brine is a common industrial process used to produce chlorine gas, sodium hydroxide (lye), and hydrogen gas.

Let's look at the other options:

* Rust is a product of corrosion, not something refined by electrolysis.

* Titanium can be refined through a process called the Kroll process, but not typically by electrolysis of brine.

* Water can be electrolyzed to produce hydrogen and oxygen, but this is a separate process from brine electrolysis.

Therefore, the substance commonly refined by electrolysis is brine.