Elemental iodine will sublimate and leave the solution.
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Sublimate means it will turn from a solid to a gas, without becoming a liquid first, doesn't it?
I can see where it might sink to the bottom and not dissolve, but could solid Iodine turn to a gas at room temperature?
As I recall elemental Iodine will dissolve in water in very small amounts.
I used to play with halogens (except for Fluorine, and I suppose Atstatine, which is radioactive and very hard to find). I gassed mice living in the cold airshafts of our home with Bromine. It killed them all, smelled weird for a day and after the deceased mice began to decay, the smell got worse.
Finally, we set up a line through the shafts by rolling a roller skate with a line on it between shafts, and then used a sandbag to rake in the deceased rodents. There were about 30 of them. The house has not had mice since then, so far as I know.