On rare occasions when a client dies, if they respawn too fast (right after they die), the killing damage that the client received carries over to their next spawn on the client's side. For example, if the client dies from a 35 HP hit, they respawn with only 65 HP. The client is apparently able to pick up medikits, but I don't think the server actually gives them to the client, since the server knows the client's true HP.
A more severe case is that if the client dies from an 100+ HP hit, the client respawns as a 0 HP player, and they won't be able to pick up any items client-side (weapons, medikits, powerups), as the client believes that the player is dead. I think the server still gives the items if applicable though. The weird behavior persists until the client is shot, which resyncs the player's status with the server.
Shows the second situation. Skip to 6:50.