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some obscure exemptionfor-profit companies do not have to pay strikers wages and benefits while they are on strike. Unions have strike funds they use for that.* When workers go on strike, they want their absence to disrupt the profit making of the business, that is their leverage; but they sacrifice to do it.
Part of the claim in this current "unionize graduate students" drive is that they do work and get paid an income to support themselves, that's why they should be allowed to unionize. I mention that because the headline "students on strike" undercuts that claim, when the grad students want to avail themselves of labor law to make it a regular worker-employer dispute.
Another point, universities are non-profits and would be better able to say "pay them with what?" if they are not working (some courts decide issues on the basis of equity, where ability to pay is factored in. ianal)
(*Did you know that most picketers you see, like next to an inflatable rat outside a real estate development or construction project, are not "employees of the site on strike", but are instead union members who happen to be unemployed from elsewhere and get paid to stand there and do it because it's some income, and helps the union.)