The Obama administration on Friday proposed immigration rules that would allow foreign-born entrepreneurs to remain in the United States for up to five years if they own a significant stake in a start-up company with the potential for “rapid business growth and job creation.” Immigrant entrepreneurs who hold an ownership interest of at least 15 percent and have an “active and central role” in the company’s operations are eligible to apply for parole, or temporary permission to remain in the United States, for up to two years.