In many areas there are restrictions to have just 10 men gather for davening. One of the situations that can arise when there are just 10 men for the minyan is that it is possible that in middle of the davening you may lose the minyan. Someone might leave to go to work or go to the bathroom. Over the next few days we will discuss the laws of continuing davening without a minyan.
1) If one had a minyan of 10 men and the 10th man left in middle of the davening, as long as there is still 6 men remaining, the chazzan may complete the “topic” that he is in middle of, however, he may not begin a new “topic”. As we shall explain.
2) If one had 10 when he began saying kaddish and people left he may complete the kaddish, assuming 6 still remain. (S.A.55:2)
3) It should be noted that for the 10th man to leave the minyan so that a minyan no longer remains is a sin. (Rama and see Eishel Avraham Botchetch as to whether this applies to kaddish as well.)

4) If one began chazaras hashatz (even the first bracha) with a minyan and the 10th man left in middle, he may complete chazaras hashatz, including the recitation of kedusha, assuming there are still 6 people remaining. (S.A. 55:3 and M.B. 15) He may even recite the full kaddish that is recited after chazaras hashatz (e.g. the full kaddish before Aleinu by Shachris and Mincha). (ibid. Rama) During Shachris where there is an additional half kaddish (following Tachanun), the chazzan may recite that half kaddish as well. (M.B. 10 & 19) [The mourner’s kaddish may not be recited, as we shall discuss in a future email. In addition, one would not be able to start Krias Hatorah without a minyan present.]
5) Although, the chazzan may complete chazzaras hashatz (Halacha 1), kohanim may not recite Birchas Kohanim, as Birchas Kohanim is perceived as a new “topic.” In Israel and for Sefardim even in the Diaspora this is a daily occurrence, in Chutz L’aaretz this would only be relevant on Yomim Tovim. Rather, the chazzan just says the brachos (the same procedure that is done when there are no kohanim present). (M.B. ibid. and Ishei Yisroel page 148)

6) If there was a minyan for the beginning of the silent shemoneh esrei and the 10th man left during the silent shemoneh esrei, the halacha is as follows. During Shachris and Mincha one may not begin chazaras hashatz or recite kaddish. However, during Maariv one may recite the full kaddish before Aleinu, assuming that 6 men remain in shul. (Ishei Yisroel page 149)
7) If there was a minyan for reciting Barchu at the beginning of Maariv and then the 10th man left, they may recite the half kaddish before Shemoneh Esrei, but not the kaddish after shemoneh esrei. (ibid.)

8) If there were 10 men present for Yishtabach or for Ashrei of Mincha (before Shemoneh Esrei) and the 10th man left before kaddish was recited, Kaddish may not be said. (S.A. 55 M.B. 7)
9) If one said Aleinu with a minyan and the 10th man left before the mourner’s kaddish, kaddish is not said. (Ishei Yisroel page 149)