In קריאת שמע there are רמה words which is 3 short of the רמח איברים. And we want it to be כנגד the רמח איברים, so the חזן repeats the words השם אלקיכם אמת, and is יוצא the צבור. When davening ביחידות we instead add קל מלך נאמן. Let's say you are davening בצבור, but you know your קריאת שמע will drag beyond the חזןs recital of השם אלקיכם אמת, should you say אל מלך נאמן before saying קריאת שמע? Even if you will argue that the words השם אלקיכם אמת don't have to be at the end of קריאת שמע, and you can be יוצא those words from the חזן while you are in the middle of קריאת שמע, but usually there is no heads up that the חזן is about to say השם אלקיכם אמת, and you are reciting some words during that time, and you can't say words of קריאת שמע and be יוצא some words from the חזן simultaneously.

ב"ה Shalom Your learned question is discussed in the Shulchan Aruch in הלכות קריאת שמע סי' ס"א סעיף ג. The שערי תשובה סעיף ב there quotes the סדר היום , written by the 16th century Kabbalist of Tzefat ,רבי משנה בן מכיר, that in a case like yours, in which you have not completed קריאת שמע, but the Chazzan has finished, you simply stand silently to hear him say ה' אלקיכם אמת Indeed, there is no heads up from the Chazzan when he will sat ה' אלוקיכם אמת, but usually the Shul is quiet enough during קריאת שמע, so that you are able to hear him. In addition, when you have a regular pace in which you say קריאת שמע you more or less have an idea where your'e going to be in your Siddur when the Chazzan gets there. All the best