Those who are the spouse of a foreign national with a certain visa status or married to a US citizen, also have options to consider.
Foreign nationals who are a “dependent” spouse with L-2, J-2, or E-2 status—that is, married to an L, J, or E visa-holder—may be eligible for employment authorization. They’d have to apply for an Employment Authorization Document (EAD) through USCIS (which, at the time of this writing, is taking six months or more to process) but upon the granting of that document they’d be eligible to work for any employer.
Currently, USCIS allows H-4 spouses who meet certain conditions to also apply for an Employment Authorization Document. Of course, if a foreign national’s spouse is a citizen of the US, sponsorship by that spouse for lawful permanent residency is an option.