If the animal is grade, it can be Recorded Grade NOA(Mative on Appearance) or NOP (Native on Production), or it can have recorded American or Purebred parents that gave it a percentage of grade- like 50 or 75. Of course, the percentage could be less if it started as a Grade Experimental. (an experimental is a cross between two Americans or Purebreds or and Americanor Purebred and a Recorded Grade.) For our sanity, I am going to pretend your animal is a percentage Grade Nubian. (The percentage will be listed on top of their registration papers.)
So if you have a 50 percent, and you cross them to an American or Purebred, the offspring will be 75 percent. If you cross the offspring to an American or Purebred then those kids will be 87.5 percent Nubian, which makes them American (7/8 Nubian). Since the herd book is closed, the offspring (from a registered Nubian buck) after that will remain Americans. Purebreds are animals that were in the herdbook before it was 'closed'.
This is from the ADGA Rules:
AMERICAN NUBIAN
Animals may be registered in this section of the herd book when they qualify under any of the following provisions:
a. When the sire and the dam are registered as American Nubians.
b. When one parent is an American Nubian and the other is a purebred Nubian.
c. Females only can be registered when the sire is an American or purebred Nubian and the dam is a 3/4 (or higher) Nubian in the Grade, Grade Experimental or Experimental herd book. The doe to be registered, as well as the dam and the maternal grandam, must be of correct Nubian type (see H. Note 1).