Is it permissible to keep items belonging to a person accused of drug trafficking, or to dispose of them, or to give them to one's parents without their knowledge of the source, and if not, what is the correct action?

If it is highly probable that the source of all his wealth is from drug trafficking, and he has no other permissible money, then accepting his gift is forbidden. Whatever he left behind must be spent on the welfare of Muslims, such as the poor and the needy. However, if it is merely a doubt, or he possesses other permissible money, then accepting his gift is not forbidden, and you may benefit from what he left behind.