I think it's possible he might stay, but only if he's allowed complete freedom to change things in his view for the future. And that'll be why he probably won't stay.
They could have offered him the earth knowing the transfer wndow had shut, buy who you like etc. If we do go down or stay up (unlikely as that is), they'll then be tested at their word and we know just how trustworthy that is. Don't see them suddenly becoming truthful after a near decade of constant lies.
Besides, going down is the perfect way to cover the lies they've probably told Rafa about what freedom he would allowed as manager. It'll be all, sorry Rafa we've got to cut cost now because YOU didn't keep us up.
Unfortunately for us, there's no cure for being a cunt, and our club is full of them.