You can't deal with these ppl otherwise UNLESS you agree with them (that they are possessed) and then perform an "exorcism".
My mothers friend mother was diagnosed with paranoic-schizoprenia (a common mental illness among old people). She convinced herself that someone is spying on her, everywhere, walks after her everywhere she goes, some kind of "FBI spies" lol. Well that friend decided to take her to a psychiatrist, but there was an issue - she'd not go if she knew where she being taken (she was as sane as ever in her own mind). So she was told that it's a heart doctor (had some issues with heart too). Long story short - she was given some drugs "to help her heart" and doctor said "Yeah, I've heard this, I actually know a few of my patients who were being spied too and I managed to solve that by speaking directly to these who are orgnisig said espionage. I will do that for you too, don't worry.".
A few weeks later that old lady was like "You know what, they stopped spying one me, that doctor probably did something to them. It's all good now.".