I have a friend whom has 2 adopted sisters that are twins, they recently turned 21.
Her Parents (she has a biological Brother too) were fostering these twin girls from 6days of age & at their 18th birthday they presented their Foster parents with legal adoption papers & had thier names legally changed to their Foster (now Adoptive) parents!

It was awesome....

So I guess it has happened but not sure of how common.... Best wishes in your plight!