What does it mean to have "undetectable" HIV? What are the risks of contracting HIV from this person?

Once a person is infected with HIV, they are infected for the rest of their life. There are NO documented cases of cures from HIV.

We assess the prognosis of a person with HIV and monitor the response to HIV treatment with a test of the amount of viral load - the plasma RNA - in the blood. When the test result is below the ability of the test to detect the HIV RNA, we say that the result is "undetectable". This does NOT mean that this person no longer has HIV, it simply means that their viral replication has been suppressed with treatment, or, less commonly, is set at a very low level in the absence of therapy.

There is strong evidence that an undetectable viral load in a person with HIV is associated with a lower risk of transmission. For example, the risk of sexual transmission has been shown to be lowest in a person with HIV when their viral load is < 1,000 copies/ml. However, that risk is NOT zero, though it appears to be quite low. Similarly, a pregnant woman with an undetectable viral load is known to have a very low risk of transmitting the virus to her baby during labor and delivery. And also similarly, the risk of transmission in that setting is NOT zero, but very low.

Most HIV physicians have patients with HIV who are one half of a discordant couple, i.e. they are partnered with someone who is HIV negative, and yet they and their partner have chosen to have unprotected sex when they are undetectable. I personally do not recommend this practice, but I understand how patients can make this choice. My interest is to provide them with the best and most accurate possible information, and then to let them make their own decisions (as they will do in any case).

My recommendation to people living with HIV and their sexual partners, whether HIV positive or negative, is to use safer sex guidelines to prevent transmission.

I urge you to talk to your doctor about your question and this answer.