A good summary is to be found in a shiur from the The Israel Koschitzky Virtual Beit Midrash.
In short, “…. ten men who prayed alone can subsequently fulfill their obligations of Kaddish, Barkhu, and Kedusha. How so? One is chosen to say Kaddish and Barkhu and the first berakha of Keriat Shema (until "Barukh ata Hashem yotzer ha-me'orot"), then he skips until Shemoneh Esrei, and begins Shemoneh Esrei aloud and says Kedusha. Since only a small piece (or "slice") of Keriat Shema is said, this procedure is referred to as "porsin al Shema."
And “This law applies as well to one who arrives late to synagogue. After saying Pesukei De-zimra, he may say Kaddish and Barkhu and then continue with his prayer. When he reaches Shemoneh Esrei, he should recite aloud until after Kedusha, then continue quietly.”
Has anyone ever seen someone do it? I have never seen it despite it being a simon in Shulchan Oruch. Is this (a) because the opportunity never presents itself, (b) because it is not practised nowdays (c) because people don’t know about it or (d) another reason?