Ah.. a native language. Well, considering a newly born individual is in need for ANY language, so yes they tend to pick up one. However, I am talking about someone who already has a L1 that isn't English. You CAN escape "picking up" English even if it's prevalent around you, like my grandmother. She got by around herself, took the bus, ran errands, etc. without knowing more than a handful necessary phrases in English.
It really depends on the individual, I suppose. Someone can become fluent in Italian while studying abroad in Italy for just a summer. However, I think motivation has a lot to do with it.
I love and admire my grandmother, but she definitely wasn't motivated to learn more English than she needed to know. 
