Cereal Rye has re-seeded itself here in Central Ohio for me. I used it on a steep bank of a pond dam, and on a bank of my new shop to stabilize the bank until other grasses took hold, even as a cover crop in the garden for a living mulch.
All was sown way beyond the recommended rate and was very thick. On the banks it reseeded itself for at least 4 years but got less every year possibly due to birds/mice eating it, or other vegetation choking it out, lack of ground contact, as is pulled into the dirt.
Here is a pic of the first cereal rye I sowed/rolled for a living cover crop. Second pic is of what came back up that Fall after running a mower over it. 3rd pic is of in May of last year and experimenting with setting cabbage plants in the rye stubble. I ended up mulching with leaves around the plants, as we got into a drought and most of the rye died from lack of water.
But do note rye was rolled the first year to terminate the rye so it would not go to seed, but apparently some had dried enough to make seed. If it had went to seed, it would have been much heavier I'm sure and had better ground contact.