It sounds to me like you got some bad information. During sex a HUGE number of sperm are released. (It’s somwhere between 100 million and 300 million) I think what you might be talking about is pre-ejaculation fluid, just like some of the other posters have said. Pre-ejaculation fluid (or pre-cum) has a very high concentration of sperm all by itself though, so it can definately get you pregnant, even if he doesn’t finish.
Also, one poster said that sperm can live up to 7 hours, but that is incorrect. Sperm can live up to 5 WHOLE DAYS in your body!