No, you cannot, unfortunately.First, regardless of the depth of your feelings for him, or your committment to each other, "boyfriend" is not a legal relationship; it is not being a spouse or in a recognized civil union. Being his girlfriend gives you no "standing," or legal right, to sue for any injuries to him or for his death.Second, it is very unlikely that even a spouse could successfully sue on this ground. An employer *may* disregard an employee's health and can ask him to stay at work even if he does not feel well: an employer is not an employee's parent or legal guardian and has no legal duty to look out for this health. Since they had no duty to take care of him, they did nothing legally wrong. Further, they did not make your boyfriend stay: he could have left (i.e. he was not imprisoned). Yes, his job could have been  in jeopardy, but  he chose to put his job ahead of his health; his employer is not responsible for his choice.