For people living abroad that wish to relocate to the US: I am aware of H1B visa sponsorship, but I'm wondering if you can be sponsored by an employer straight for a green card? If it is, presumably it happens exceptionally rare and it comes with many strings attached in the employment contract.
Yes it certainly is possible - just look up the EB visa class.
Every fiscal year (October 1st – September 30th), approximately 140,000 employment-based immigrant visas are made available to qualified applicants under the provisions of U.S. immigration law. Employment based immigrant visas are divided into five preference categories. Certain spouses and children may accompany or follow-to-join employment-based immigrants.
It can be a fairly long, drawn-out process - and the requirements on the sponsoring company are more arduous than those for a similar H-1B worker.
I am currently working through the process of an H-1B to EB-3.
Whether or not there are strings attached to an employment contract depends almost entirely on the sponsoring company.
In my case there are none. My sponsor appears to prefer using the carrot instead of the stick to try to ensure that I'll stay around and make their investment worthwhile.
Yes. You don't have to be in the US or be working for the company that petitioned you to be petitioned for employment-based immigration. Employment-based immigration is based on an offer of future employment (i.e. after you immigrate). As long as the company offers to employ you after you immigrate, you qualify for employment-based immigration. It's just that most of the time, companies are not willing to go to the expense and hassle of petitioning somebody if that person is not working for them inside the US, especially if there is a wait for visa numbers for the person's category and birth country.