willfully remains

The conduct proscribed is the affirmative act of willfully remaining, and the crucial word 'remains' permits no connotation other than continuing presence... it is true that remaining at the instant of expiration satisfies the definition of the crime, but it does not exhaust it... we believe an alien 'remains,' in the contemplation of the statute, until he physically leaves the United States. The crime achieves no finality until such time.

Defined by the Supreme Court in - United States v. Cores, 356 U.S. 405 (1958).