The sentence comes from the song 'Why do I feel so bad'.I wish that I could stay
In the song, I don't like change. But in time things would change. So I feel bad.
I make the sentence myself. I want to go on a trip but I can't. Because I don't have money and I have to go to school.I wish I could go on a trip.
Form=subjective+wish+(that)+past tense form (would/could/were....)
I wish I could buy a bicycle.
I wish I could see the sight.
I wish I were a rich.
I wish I had a car.
I wish I would study hard.
We use 'wish' when we want to do something but we can't do that. And we use it when we suppose what we want to do in opposition to present fact.