When the recital of Kaddish in a minyan has begun, and a few men leave in the middle, if most of the minyan remains (at least six including the chazan) the Kaddish may be completed. This rule applies to all prayers that require a minyan; if they started to pray with ten people and most of the minyan remained, they conclude the prayer that they started, but do not begin a new prayer (Shulchan Aruch 55:2). It is prohibited to walk out and disband the minyan in the middle of matters of sanctity. However, in situations in which it is necessary, one is permitted to leave before the start of the next part of the prayers.
If a minyan began Chazarat HaShatz, and part of the minyan left but most remained, those remaining may say Kedushah and conclude the repetition of the Amidah. However, they do not say Birkat Kohanim because it is a mitzvah by itself. Concerning Kaddish Titkabal after the prayer service, the poskim are divided. The Sephardic custom is not to recite it since it is considered to be the start of a new prayer. According to the Ashkenazic custom it is considered to be the end of the prayer service because in it, we ask that our prayers be accepted. Therefore, in Shacharit and Minchah, if there are ten men at the start of Chazarat HaShatz, they may recite Kaddish Titkabal. (In Shacharit they also recite the Half Kaddish before Ashrei.) In Ma’ariv, if there is a minyan at the beginning of the silent Shemoneh Esrei and six men remain, they recite Kaddish Titkabal (Shulchan Aruch 55:3; Mishnah Berurah there).
