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I think there may be a difference between someone finding a job that is a native speaker of English and one who is not. Her English is good, but it's not the same as say a Canadian or someone from the UK coming here. I think there would be some barriers.
I guess - but I dunno, based on what I've seen.
Three examples, concerning Russian women I know.
#1). Spoke excellent English upon arrival - had no problems getting multiple job offers before she even got her EAD. Found these jobs through traditional classifieds and on-line job postings, and one from a flyer I got at the post office and brought home. Ended up working at the post office for all of 1 day, before quitting to take a job at the university as a "fiscal admin assistant" ($30K/year, outstanding benefits) within a few weeks of having her EAD in hand. This person has since taken two undergrad courses (Public Speaking and Financial Institutions & Management) before enrolling in a graduate business program, and has completed a total of 18 credits with a B average.
#2). Spoke poor English upon arrival, took some ESL classes. After being here for a year, took a 5 month course in phlebotomy. Got a part time job in this field ($14/hr) almost immediately. Found job-listing on-line. Still speaks not great English - I have problems understanding her much of the time.
#3). Spoke NO English upon arrival, took some ESL classes. After being here for a year, took a 5 month course in phlebotomy, graduated #1 in her class, got a full-time job, $12/hr with benefits (including education benefits) almost immediately thereafter. Found job-listing on-line. Speaks pretty good English from what I can tell, I understand her most of the time.
So, just based off what I have seen, what it takes for a new immigrant, regardless of their level of English, to get a job, is personal initiative and motivation. "Special programs for new immigrants" are not required.
Just my observation (:
Cheers!
AKDiver