The most recent term was preference relative, which is defined as:
An immigration term, preference relatives means the married children of U.S. citizens, children over 21 of U.S. citizens, the spouses or children of green card holders, and brothers and sisters of U.S. citizens where the U.S. citizen is at least 21 years old.
Preference relatives must usually wait to get a green card, because only around 480,000 green cards are available to preference relatives in total per year. Preference relatives wait in line based on their “priority date,” which is set when their U.S. citizen or permanent resident petitioner first filed a visa petition for them.
Jeffrey's guess was awfully close.
Today's term is:
As always, no dictionaries please.