Auto Fuel injection Question ???

I went to two years of auto mechanics school so long ago that only the
Chevrolet Corvette had fuel injection back then in 1965  I just thought
of a question that I am surprised I never thought about before, It is
when you take your foot off the gas and cost in a fuel injected car does
the fuel injection Stop ?
And if not why not ?

Please send a cc of your answer to me at Ranger116@webtv.net

Thank you

Tom Buyea, Miami, Fl.