Here martyred describes a look or expression, not a death. A martyred look is an unhappy face put on so that other people will feel sorry for you — as if you are bearing a heavy load and everyone ought to notice. “She gave him a martyred look” means her face said “see how much I put up with.” It is a little sharp and a little funny; you use it when you think the person is laying the suffering on thick. The feeling comes from the picture of a martyr, but this use is about acting, not about dying. Though actually the same spelling is also the ordinary past form of martyr, “killed for a belief”; this sense is the face that asks for pity.