How do Biblical Unitarians understand what some theologians refer as the Kenosis in Philippians 2? Philippians 2:5-9 describes the attitude of humility, love, and service which Christ Jesus possessed while on earth:

Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men. And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross. Therefore God has highly exalted him and bestowed on him the name that is above every name...

There is much already said about what it means to &quot;be in the form of God&quot; and &quot;equality with God&quot; in the literature of both trinitarians and non-trinitarians.  See here for a start.  This question is not about those particular aspects of what some theologians, in expounding this passage, have termed &quot;the Kenosis&quot;.
The question is regarding the notions of &quot;emptying&quot; and &quot;taking the form of&quot;.  The passage seems to present that in order for Jesus to be found in the form of a servant he needed to empty himself.  More specifically, it states that he emptied himself by taking the form of a servant and being born in the likeness of a man.
If Jesus did not pre-exist his birth then:

By taking the form of a servant and being born in the likeness of a man he emptied himself of what, exactly?

How can one empty oneself by birth as a man if one does not pre-exist that birth?
Caveat: this is a difficult sentence in general and there is no settled translation.
However it's translated, it's easy to make a subtle assumption about the text that isn't actually there (although a straightforward inference coming from a trinitarian position).
In the article Philippians 2:6-8 the authors conclude

&quot;The verse is not speaking either of Christ’s giving up his “Godhood”
at his incarnation or of his God-nature being willing to “hide” so
that his man-nature can show itself clearly. Rather, it is saying
something else. Scripture says Christ was the “image of God” (2 Cor.
4:4), and Jesus himself testified that if one had seen him, he had
seen the Father. Saying that Christ was in the “form” (outward
appearance) of God is simply stating that truth in another way. Unlike
Adam, who grasped at being like God (Gen. 3:5), Christ, the Last Adam,
“emptied himself” of all his reputation and the things due him as the
true child of the King. He lived in the same fashion as other men. He
humbled himself to the Word and will of God. He lived by “It is
written” and the commands of his Father. He did not “toot his own
horn,” but instead called himself “the son of man,” which, in the
Aramaic language he spoke, meant “a man.” He trusted God and became
obedient, even to a horrible and shameful death on a cross.&quot;

So it's not that there was time 1 'he empties himself' time 2 'he is born'.
To answer the questions

He emptied himself of all his reputation and the things due him as the true child of the King. He lived in the same fashion as other men.

&quot;How can one empty oneself by birth[?]&quot; The text doesn't quite say this, and Young's literal translation reads &quot;but did empty himself, the form of a servant having taken, in the likeness of men having been made&quot;. So the Biblical Unitarians in the article quoted above would say it's a misreading of the text. The emptying doesn't happen before, or really even starting with his birth, but at some point in his life (presumably with a gradual increasing awareness as he grew up that he was the Messiah), most notably dying on the cross.