I've seen people bring this up before--a woman they're into texts them every now and then when she wants to feel better about herself, even though she has no intention of dating this guy.
My question is: How does one handle this? What do they say (or not say) to build interest in the woman?
It depends, if I'm in a sex-relationship/friendship with that girl, or working on something similar then I'd text her back and give her some attention.
But in these cases I'm always slow with texting back, I'm not sending instant replies, always take 5-10 Minutes before I reply, and I never reply faster than she did. That gives her the impression that you're giving her some of your very valuable time, and that she can't take it for granted.
And I always pretend that I'm busy with something very interesting, amazing, whatever, I'd never give her the impression that I could be bored too. -> DHV and it again makes it more valuable that I took the time to message her back, AND she doesn't get upset if you're replying slowly, cause you're busy.
And don't let her play games with you, IMHO women like that often have some issues, don't get too deep into her world, cause then she'll draw you into her issues too, and shortly after loose respect/attraction to you cause you're no longer the guy who stands above everything, who's living a fabulous life, etc.
At least that's how I handle them actually, no guarantee that there aren't any better ways