To run out is to use the last of something. Milk, money, patience or time.
It takes of for the thing exhausted, so running out of petrol is the full phrase, and running out on its own means the supply has gone. There is a second sense about expiry, since a contract or a passport runs out. And a third in cricket, where a batsman is run out. Running out on somebody means abandoning them, which is a different and much colder thing.
1phraserun outTo use up the whole supply of something.
“We are about to run out of coffee.”
2phraseendTo come to an end or expire.
“The lease will run out in September.”
Also accepted in games: run out of
runout Deverbal from run out.
Etymology from Wiktionary, CC BY-SA