Fred: The foster style slug, which resembles a minie ball with the hollow base, is " front-heavy", like a badmitton birdie made of lead! At low speed its wobbles from side to side, and when it is not spun by rifling, its not going to be very accurate. The loads used by modern manufacturers are in the 1300-1500 fps range, with some higher and some lower. That gets the slug going downrange fast enough that it covers some distance before it slows enough to begin to wobble.
My friend designed a hollow based slug with a twist, to provide axial stability. That shifts the center of gravity of the slug back to the center of the length of the slug, and with another trick, he stabilized the slug in flight, too. I am not at liberty to disclose what he did, obviously, but I can attest to the accuracy of the slugs.
He has a letter from ATF dated in the 1950s, when he asked permission to rifle a shotgun barrel for use with slugs, and was denied. When Hastings came out with their rifled barrels, he wondered what was up? So did others, and Hastings eventually published a full copy of a letter it has from the ATF director dated in the 1980s, explaining that agencie's " new " interpretation of the definition of a shotgun, in SHOTGUN NEWS. The Hastings barrel has the same ROT in the rifling that my friend had worked out back in the mid to late '50s. HE HAS KEPT THE TWO LETTERS TOGETHER IN A FOLDER to show to people who ask him about it.
In the late 90s, he changed some of the dimensions of his slug to fit the new rifled slug barrels, and still can out shoot any other slug being made.
As to tails on Foster slugs, the first problem is finding a way to attach anything that will stay attached in flight. The second is determining how much weight, size, and shape the tail must have to give maximum affect, if any. The third, is finding some way to pack the tail behind the foster slug so that it deployes equally each time a slug is fired.