I can make an attempt at answering "what it means" with Hashem's help, however I don't know what you mean by "is there a halachic source" as what would the halacha be? If you could clarify that, I will try to help with that as well. I think trying to fit this into a practical, rigid/logical way of thinking is going to cause problems as this is a more esoteric concept.
The concept behind this idea is that Hashem's Essence is not that of a "creator", that's very "out of character" of Him. The Alter Rebbe writes in Torah Or, Megilat Ester 99B:
The fact that all the worlds are brought into existence by God and
receive their vitality and sustenance from Him - this is not the
essence of what God is. For as we say "You are who You are before the
world was created, and after the world was created" -
exactly the same. Also, if God would not create the worlds, all would
be the same regarding Him.
A down to earth way to understand this is that He is Himself, thoroughly and magnificently. E.g. when He loves us, that's Him Himself loving us; the love is expressing His eternal, pure, perfect, unchanged self, completely and utterly - who He is. A mashal for this might be a human father's love for his son. The love doesn't change him at all, in fact, the love is actually the most authentic revelation of the father's truest and deepest self.
I bring this part first, to ensure we understand the next part correctly and avoid an incorrect understanding. When "all is gone" can be understood by looking at a great ma'amer by the Rebbe Rashab called "VeYadata". The link provided is an english translation and I encourage it to be read in full.
I will summarise what is necessary for this question God willing. The idea that "Hashem is HaElokim" teaches a profound lesson. In life, we have this concept called a mashal, which is a way of dressing up a deeper idea in a more superficial one, because the latter is easier to understand and allows us an entry point into understanding the deeper idea. Sometimes we have several layers of this: we dress intellectual concepts in words, and we dress words in letters. Note how there bares no resemblance at all between the deeper "concepts" and the "shapes on the page", yet they accurately carry them and serve as a perfect vessel for them without any loss of original information.
The Rebbe explains that the whole order of creation, which, like links in a chain, starts with Hashem's Infinite Light, and gradually, through sefirot and worlds, step by step like links in a chain, take the deepest of the infinitely deep, and make mashal after mashal of it until we get the physical world. The key point is that it is an absolutely lossless process, and everything of the original Nimshal makes it down to the lowest step, even if it is way beyond direct recognition.
So really, there is no difference but we see a difference. This is referred to as "two de'ot" by the God of "De'ot". The process of gradually undoing this and having the mashal and the Nimshal become one is the כִּכְלוֹת הַכֹּל process. The end result is Hashem, who never changed, but not because we didn't mean anything to Him, but He and us became one perfectly - us becoming included in His Oneness doesn't change Him at all, because what He gave to us all along was Him, Himself, without any loss or change, and we became one with Him there and became included in His life - again, something that doesn't change Him.
Even then, when "all is gone" because He and we are One, He will reign supreme!
This is something worth contemplating silently to oneself than trying to put into words, but for further reading I recommend starting with this amazing Olat Reiyah.