What does this mean exactly? “The axe goes to the wood where it borrows its helve”

It seems to describe in some way a cycle of life.

The helve is the handle, without which the axe cannot function.
The life of the axe is to cut wood.
An axe must be used to cut wood to make the handle.
Is this what's called a vicious cycle?

I don't know if it simply means the dog bites the hand that feeds it,
or if it's something more complex.

Is there

well, thank you! I thought that this saying may describe someone that would be somewhat cruel and unthankful, because the axes had benefited from the wood, and turn out to harm the wood. But it seems that Westerner emphasize the axes was born to cut the wood, that's its nature, no personification.

You could be right. "Goes to" is a bit ambiguous. There may well be personification involved.

Do you know what language this saying originated from?
Perhaps someone will turn up who is familiar with it.