I think it depends on how well you get along with that person. It's not necessarily about "Oh - he has HIV, he's a terrible guy"
I was dating a guy, and his ex ended up getting HIV, but because he was sleeping around with other people. Luckily, he found out he didn't get it when he got tested. It's really scary, I didn't think it was as common as I've found out...It's tricky to answer...hmm.
The reality is, most people born with HIV tend to jump from relationship to relationship as soon as it starts to get too serious/vulnerable for them, or they tend to stay in that one ****ed up relationship despite any manipulations, abuse, and shortcomings. It's rationalized as "who else is going to love me despite my disease?" and the thought of breaking up to building another relationship all over again, only to be shut down once the other half finds out they're HIV+ is utter hell.