If the blood on the clothing has been exposed to air and has solidified, then there is zero chance of you becoming infected.

Strange as it may seem, air is the most efficient means of killing HIV – so once it is exposed to air, HIV can only survive for a matter of minutes.

The only circumstances in which HIV will survive outside of the body is if it is kept warm and moist in some sort of airtight container .. such as a syringe / hypodermic needle.