应该可以。只要不是被fire

我在一个公司做了9年的contractor，最后公司的信上就是写的，因为budge restrictions on ..task..., your employment with ***. will be terminated effective June 10, 2011.  You are leaving the company in good standing and are eligible for rehire.  

已经申请了EI，到现在拿了4个星期了。