Earlier quoted context omitted.
In the 1980s, getting HIV was a quick death sentence. In the 2010s, getting HIV means that you are likely to live until... Your 70s. (Assuming you have access to medication.) The problem is that you need to take expensive medication for the rest of your life. And that you can infect other people.
The infecting other people is mostly theoretical. As far as I know there is no actual instance of transmission from a person with an undetectable viral load on antiretroviral drugs to an uninfected person.
Thus, if someone is undetectable but then their treatment fails, they would become detectable and able to transmit the virus. But they could still infect someone else before they discovered their treatment failed.