Black Sunflowers

I have a friend who had sunflowers come up with no petals, just the black seeds. Some of the heads are malformed also. There are just a few plants like this; the others are okay. This sunflower patch that self-seeds every year. I was wondering if you knew why this happened and should he dig them up.

I am not sure why a small percentage of plants in your friend's garden would turn out to be missing ray-florets. My guess is that they are sports (spontaneous mutations) that have managed to persist from generation to generation. However there is also evidence that sunflowers can cross with related species to produce that are missing ray-florets. In a study (https://www.doiserbia.nb.rs/ft.aspx?id=1018-18060849045S) common sunflowers (Helianthus annuus) were crossed with a perennial sunflower, Helianthus divaricatus, to produce the ray-floret-less plants. There are some pictures in the report, and if you can imagine the flowerheads turning into darker seedheads, this may well be the way your friend's plants are producing "black sunflowers".
In Ontario, it is quite common to find perennial sunchokes (aka Jerusalem artichoke, Helianthus tuberosus) which, if they happen to grow near your friend's patch, may be crossing with your friend's sunflowers and producing plants similar to those described in the study. I don't know for sure if H. tuberosus and H. annuus can actually cross and produce fertile seeds (similar species often cannot cross), but after seeing the Indian report I would have to suspect that something similar could be happening.
Should they be dug up? I doubt that this is a disease problem, so digging up to prevent a disease outbreak is not a factor here. If the ray-floret-less plants are unsightly to your friend than yes, perhaps removing the rogue plants will help reduce the chance that similar plants will come up next year. However, the black heads could well be quite a novelty that's worth keeping; so my inclination is to just let them keep coming.