No yards with old iron around here. Scrap prices got so high in the late 70's that just about every yard went to a 5 years old or newer policy. Everything older went straight to scrap. That 5 year limit is probably a little higher now, but that was it. Lots of cars went away, including people stealing old cars just to scrap them. A friend had a '60 T-Bird disappear out of his parent's garage. The scrappers weren't real fussy about paperwork either.
Scrap prices are still high enough that a lot of cars get scrapped. If it's a big car with a cat con on it, you can get $200.
Occasionally, you will see an older car pop up in a "Pick and Pull" type yard, but it has expiration date on it where it gets scrapped after sitting for a certain number of weeks.