Extreme feather for the ultrakey or transparent parts of an image or video?

Frequently while working on some special effects, I may have an image that's been on green screen, but the green screen has been removed with ultra key, alternatively I might have an image like a PNG with transparent portions.

I often wish to feather the edges of the image to an extreme measure until the image is gone. I do not want to blur the image, I simply want to feather and choke the edges all the way down until the image is gone.

Ultra key has a feather and choke feature, 100% only accounts for about 10 pixels. I want to feather the entire screen out of existence. How do I do this? On Final Cut Pro 7 this was an easy feature because Feathering was infinite.