Single-player does persist on death, and while things do drop at your body when you die, you don't want to leave it sitting too long or it will despawn.
Shit despawns if you leave it alone and out of draw distance long enough. We lost an AK the first time we found one because we didn't want it at the time, but when we came back for it about an in-game day later it was gone. Oddly enough, the second time we found one we waited about 3 days and it was still there when I finally had the inventory space to pick it up (I wasn't going to drop a stack of morphine for a stupid gun, gotta get my fix mang). So the despawn rate could be variable.