Last we see him alive is jumping out of a jeep as it is pulled to the tunnel during 'The Incident'. From there, all we know(Unless Jack's plan is successful) is that he ends up in the Swan hatch where he paints the island of the map, and later commits suicide. Unless... Is it possible to say, that perhaps this is not the true story?
What if it was in fact an other that had been placed in the swan, maybe his name was 'Kelvin'. Who we know as Kelvin, pretends to be Radzinsky with the real Kelvin, and being an other, knows the language of latin which he writes on the secret map of the island. Kelvin is new to the island, but learns Radzinsky is lying about who he is, and as he conftons him, he enters a struggle with the other and ends up having his brains blown out. "Kelvin" then takes on the identity of Kelvin, should anyone come looking for him. He believes Desmond might be able to replace him, and makes him think the sickness is real. He on the other hand knows enough of the island to know where Desmonds boat is to try and escape, meaning he had been out and about enough(maybe).
But what of the real Radzinsky? Locked away in a certain psyche ward repeating the numbers over and over again. But he was Leonard who served with the austrailian in the army. Maybe Leonard went to the island after hearing the numbers, and was on one of "Jacob's lists". He then joined the others and does some swan work. Crazy Rad eventually replacing him(aye, me war wound)
It has holes in it but anything's possible