A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

live off something • live on something
live off something —
1
. use smth. as food: Some animals live
off plants, whilst others live off other animals. 2. get enough
food or income from smth.: He had lived off his vegetable
patch on the farm and off the sales of some cattle.
live on something —
1
. eat certain food as one’s regular diet:
They live on fish, coconuts, and tropical fruit — papaya,
bananas and mangoes. 2. = live off something 2: Maugham
knew that he had to court popular taste if he wanted to live
on his writing.
live off the fat of the land • live off the land
live off the fat of the land —
1
. use products that one grows
for one’s food needs: They share a dream of a little place of
their own, where they can “live off the fat of the land.” 2.
enjoy a comfortable lifestyle: He was pretty fed up with these
bloated royalists who were living off the fat of the land and
off American aid.
live off the land —
1
. = live off the fat of the land 
1
: Thousands
of Mayan peasants live off the land in the Yucatan, growing
maize — a world away from the beach resorts of nearby Can-
cun. 2. be able to survive from what one finds in the wild:
Liv ing off the land requires that you get very close to that land.
Axes, shovels and fishing gear will be essential to your survival.
live out something • outlive something
live out something —live to the end of a specified period of
time: He was as certain as any one possibly could be that the
chap could not live out the week.
outlive something —
1
. continue to exist beyond smth.: Ms.
Bork argues that the Association has outlived its utility as the
principal forum for addressing region-wide issues. 2. = live
out something: Besides secrecy, speed was of the essence —
“according to all intelligence” the Spanish King could not out-
live the month of October.