We did this as kids several times in South Texas. After the farmers harvested, we would ride our dirt bikes to a nearby field with paper sacks and gather the produce that was literally at the corners of the field which the machinery missed as well as where it had been loaded into the trucks and spilled over. My memory is a bit vague, but we I remember carrots, cucumbers, and corn specifically, and I remember my mom and aunt making pickles with most of the cucumbers. As far as asking permission, the kids didn't do this, but I suspect that my aunt or uncle knew the farmers because he was the only vet in a small town and they knew everyone.
I believe the sod farms out west of town allow people to purchase the edges for almost nothing, but I haven't heard anything about that in years, so I don't know if they still do. But your question has me thinking about the potential of this for the poor in the community. Wouldn't it be great if CalOrganics allowed representatives from the Salvation Army to glean OR if they would contact the SA when their clients could come glean? What do you think?