I'm not sure I understand what you're asking. I was trying to say that, IMHO, programs do not offer "pity" interviews -- i.e. we do not invite people whom we have no chance of ranking simply to make them not feel bad. The only exceptions might be:
1. Home program -- I expect some home programs invite most of the students from that school to interview, even if they are unlikely to make the final list.
2. Away rotation -- some programs might interview all away rotators, but many will not.
3. Politics -- if someone is "connected" enough, I guess they might get an interview.
4. MSPE / Late application submission disaster -- many programs start inviting candidates before the MSPE. Rarely, someone who looks fine prior, has a poor MSPE. Since the person is already invitied, programs usually don't tell them not to come. However, in this case, these applicants probably have some chance of getting on the final list, so all is not lost. This is rare, before everyone starts panicking about their interviews they have already booked.....
If you get an interview, then you