。
She still believes her son is alive.
Literal
[topic-は] still son [subject-が] is-living [quotative-と] is-believing.
Three layered states: 生きている (resulting state of 生きる, 'is alive'), 信じている (resulting state of 信じる, 'is in a state of believing'), and the と marking the embedded content of belief. Together: 'still in a state of believing that [her son is in a state of living].' The quotative と marks both spoken speech and the content of mental states (think, believe, feel). The sentence's emotional weight comes from the implicit context — usually meaning someone has gone missing or is presumed dead, but the woman maintains hope. A recurring theme in disaster, war, or missing-person narratives.