Don't go out unless absolutely necessary. - great Don't leave home unless absolutely necessary. - great Or I should say, Don't go out unless it's absolutely necessary. - also great Don't leave home unless it's absolutely necessary. - also great Summary: Great :) Use them all as you wish,. PS had to loook up "elided" - technical word. Was beyond my experience. Might want to limit its use to language lessons. :)

They are both correct, but it sounds natural in conversation to add the "it's". The first one would be mainly as a public announcement, if you are making something like a poster which needs to be formal.

All four sentences are entirely correct, the "it's" being elided but understood in the first two.