All the other answers seem good. I just add one more relating to "with an adjective". I think "stay" can be used as a noun, but maybe not "remain".
"A short stay" uses "stay" as a noun.
I can't think of any way to make a noun out of remain however.
She is in hospital, but her stay will be short.
She is in for a short stay in hospital.
But, she must remain in hospital for a short time.