参考答案及解析:
1. with—without。根据illegal aliens的定义，应该是people living in the U.S.A without proper authorization
2. until—when。从逻辑意义上来分析，是Others....did not leave when their visas were expired（当签证到期时他们也不离开美国）
3. possible—impossible。从上下文的说明判断，要弄清楚到底有多少非法居住在美国的外国人，或得一个确切的数据是完全不可能的
4. ranged之前加have。因为是指did not leave until their visas were expired. Recent estimates而不是以往的estimates
5. affected—affecting。此处相当于（a new law）which/that affect illegal aliens
6. have—had。用过去完成时，因为整个句子讨论的是过去的事，并且此处具体指country since January, 1982 to gain legal status if they applied by May 4,1988
7. encourage—discourage。如果为encourage则与全文的逻辑和意义矛盾
8. 在difficult之前加it。making it difficult for undocumented people to find employment，其中it为形式宾语，实际宾语为不定式短语（for undocumented people）to find employment
9. providing—provides。provides for severe penalties与prohibits American employers from hiring illegals 为并列谓语，而不是与hiring illegals并列
10. number—numbers或在large之前加a。习惯为numbers of或a number of