I think that's kind of a malformed sentence. Programs themselves do not suffer or not suffer from the halting problem, it is only a problem when considering the space of all programs.
It's not malformed, it's just incorrect. Additionally, the halting problem is about provability. That sort of imprecision of language needs qualifiers at least.
I also think some programs can suffer from the halting problem. I mentioned above properties of the decimal reprensentation of pi (like is 123456 in pi)