The phrasal modal is used with nothing following it, when the verb it refers to is clear from the context.
'It's not really improving anything.' 'No but perhaps it's not meant to.'
I've never had a tremendous social life; I tend not to put that first. I ought to, but politics comes first.
It's a great concept but I don't think it is foolproof, it doesn't blur some faces and number plates like it is supposed to.
I wish I could run about like I used to, and I love dancing. Well, I can't do that any more.
In the case of would rather and would sooner, the phrasal modal is usually followed by not, and the pattern is MODAL not.
be able to had better be bound to be going to have got to have to be meant to ought to would rather would sooner be supposed to be sure to be unable to used to
'Don't tell me if you'd rather not,' he said.
They'll be delighted if you'd like to come, but of course we'll understand it if you'd sooner not.