Poderia ser "My Little Runaway" por BlueRowley na FanFiction.net?
After Harry Potter runs away from his relatives' home for the sixth time, Albus decides something drastic must happen. Instead of sending a friendly witch from family services like he had done before, he sends Severus Snape in hopes of scaring the boy into staying put. But when a storm interferes with plans, Severus realizes why Harry runs away and a change of plans ensues.
Snape move Harry para Hogwarts, onde ele o esconde de Dumbledore. Eu me lembro de partes onde ele compra algumas coisas para Harry, como o cobertor.