Thank you for your inquiry. From what we gather from the question, you were asking about the possibility of HIV transmission through touching a piece of clothing that was contaminated with blood. From the information provided, this scenario is determined to be No Risk (HIV transmission is not possible in the given scenario).
HIV (contained in a body fluid such as blood) is extremely sensitive to the outer environment. Exposure to oxygen in an environment outside of the body causes HIV to undergo a rapid reduction in concentration (1). From the CDC, HIV that may be contained in a fluid (in this case being the dried blood stain that was on the piece of clothing), has a rapid (within several hours) reduction in concentration of 90-99% (1), rendering it inactive. Furthermore, this situation does not meet the requirements for the HIV Transmission Equation (see image below), as the graze on your finger would not have permitted sufficient access to your bloodstream through a High, Low, or Negligible Risk activity.
Recommendation: There is no evidence or no documented cases of transmission. Refer to a healthcare professional for more personalised answers or other health-related questions.
All the best,
AIDS Vancouver Online/Helpline, Shirley
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(1) HIV Environmental Exposure