Written by Horav Yosef Yeshaya Braun, member of the Badatz of Crown Heights
There’s a machlokes Rishonim (a dispute among early halachic authorities) regarding what to do if one is in middle of Shemoneh Esrei and the chazan has begun reciting Kaddish or Kedushah. Some Rishonim maintain that Shemoneh Esrei should be interrupted and one should reply along with the minyan, whereas others argue against it.
The halachah codified in Shulchan Aruch is a compromise: one should pause and listen passively as the chazan says Kaddish or Kedushah, thereby being yotzei (meeting one’s obligation), and then proceed with reciting the Amidah upon their conclusion. Of course, this applies only if the one davening can hear all the words that the chazan is saying, though there are those of the opinion that hearing any participant in the minyan say “Amein” or “Kadosh, kadosh” is sufficient.
Some suggest that it’s also necessary for the chazan to have the intention to be motzi the people who can’t respond verbally. However, most poskim don’t seem to agree with this requirement.