What is the ruling on an engineer paying the costs of a worker's surgery from the company's money without the sponsor's knowledge, and would he be sinful if he complied with the sponsor's order and the worker died?

Your action of saving the worker and providing him with treatment is correct and rewarded, based on the Almighty's saying: "And whoever saves a life - it is as though he had saved all mankind." Had you not done so, despite your ability, you would have sinned. It is obligatory for anyone who sees a person in need of rescue to help him; otherwise, he would be sinful. As for your claiming the cost of treatment from the company without the owner's knowledge, we hope there is no objection to that, because it became binding upon the company owner by virtue of the contract. If he refrains from fulfilling it, it is permissible to obtain it from his wealth without his knowledge, under the principle of seizing one's right.