verb
manage to support oneself or make a living with difficulty.
“Eke” is to supplement or lengthen. That’s why we say “eke” out: because we’re pointing to an activity that supplements something meager. The popular use of “eke” is a malapropism, in which the writer has in mind the concept of “squeaking by”. The literal meaning of “eke” is as an adverb meaning “also”. You eke out an existence by doing something to supplement a meagre original. You might eke out your social security income with a part time job, for example. Strictly speaking, you can’t eke out an existence by being just on social security and nothing else. “ Eke “ is all about an addition.
You will disagree of course, and point to the current usage, which is dominated by undiscerning illiterates who set no value on clarity in language. Don’t even try with me; I won’t be impressed.