Yo leo tus cartas
is it correct to use sus instead of tus in the sentence "Yo leo tus cartas"?
Yes, "sus" is correct for the second person in formal speech (both plural and singular) and for the third person plural. So, it may mean "I read your letters" (letters from "you"), "I read your letters" (plural, i.e., letters from "you all"), or "I read your letters" (letters from "them"). And keep in mind that in some countries, like Colombia, people often use formal speech even with their close friends and family members.
Unless you were in a formal conversation where you were using the usted form with the person you were talking to, you wouldn't use sus. If you were in a situation where you were forced to use the formal form ( for example, a boss wou you would never use the tu form with) You would be forced to use sus. But with everyday friends you would always use tus.