In The Kite Runner, why would Hassan jeopardize the safety of his family in regards to the items found in his hut that belonged to Amir?
Hassan's loyalty to Amir, his honor, and his selflessness define his character. These attributes trump any fear he may have for his own well being or that of his family. Because of this loyalty, Hassan admitted to stealing Amir's watch and the money, knowing Baba would believe him whether he said 'yes' or 'no.'
If he'd said no, Baba would have believed him because we all knew Hassan never lied. (91)
Hassan lied and said he stole the watch and money because he knew the repercussions for Amir, with respect to his (Amir's) relationship with his father (Baba), would be disastrous. During Baba's interrogation and eventual forgiveness of Hassan, it becomes clear to Amir that Hassan knew everything: that Amir had witnessed the rape and done nothing. Amir then imagines Hassan begging Ali not to give up Amir's secret to Baba. The implication here is that perhaps Ali knew Hassan was covering for Amir and this was a way for them to part ways and start with a clean slate. Clearly, it had become difficult for Hassan to even be around Amir, and it's possible that Ali saw this as an opportunity for he and his son to start new.