If the printer in your residence runs out of paper or toner link, you should Submit a Request, which will notify the Peer Technology Specialist team, who can refill it.
In most public spaces (Lathrop, Green Library, etc.) there is someone on staff during all business hours, who can refill the printer.
If they’re not handy and/or you’re in a rush, you can release your print job from any other printer on campus. See https://vptl.stanford.edu/student-resources/printing-resources/printing-help/print-faqs for more information on how to pick up your print job from any printer.