A person who has graduated from Juilliard.

In the United States, the Juilliard School in New York is the most famous of all music conservatories (college-level schools). In the U.S. the name "Juilliard" is instantly recognized. You would expect a Juilliard alumnus to be on course for a successful career in music, so it is sad and surprising to hear that one of them "is now homeless," much as it would be sad and surprising to hear that a Harvard alumnus is homeless. As others have noted, "alum" is informal for "alumnus" or "alumna," a person who attends a school. Two details: 1) there are two completely different words, with different pronunciations, both spelled "alum." When it is short for "alumnus," the accent is on the "-um." It is also the name of an astringent salt with medical uses, pronounced "AHL-um." 2) Many native speakers mistakenly believe "alumnus" means "graduate." It does not; it only means "former student." Thus, Bill Gates can be accurately called a Harvard alumnus, even though he did not graduate.

Shaunah is totally right: it's refering to a graduate of Julliard. It might be interesting to note that "alum" is a shortening of the LATIN word "alumnus"(male)/"alumna"(female). Although English doesn't really bother with gender in (most) words, anything taken from Latin (which is often used when talking about academic terms) often still carry the genders. I think English speakers will use the word "alumni" and assume it is singular and plural and used for both male and/or female graduates (when it is actually just the male and plural form).