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An alien can of course apply for work in the USA without actually having a work visa. However, she would need to get it prior to beginning work. This means that the employer must be willing to file for the visa on her behalf in most circumstances. This limits her ability to find work unless the employer is willing to do this, and since this can be both time consuming and expensive, it does handicap her somewhat in her job search.
So in other words, she can apply for work, but cannot actually work until a visa is in place. Because of this, most of the time, the employer is already in agreement to hire and helps to file for a work visa while the alien is still abroad.
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