Former supervisor encouraged me to apply for a role at her new company

My former supervisor moved to a new position at another company a couple of months ago. She recently reached out to me to let me know of an opening coming up in her new place of business that she thought I would be perfect for. She just sent me the job description, and I'm very surprised to see that the stated salary range is well beneath what I'm currently making. It's so bizarre to me. My supervisor would know exactly what I'm making in my current role, and I'm wondering why she would think I would want to take a lower paying job? I'm considering writing back to her something about how it sounds like a very exciting role, but that as a rule, I only apply for roles that are a step up in salary and see what she says.