'sad prospect' is correct and usable in written English.
You can use it when you want to describe a situation or outlook that seems desperate or disheartening. For example: "The future looks like a sad prospect, with the economy in freefall and millions of people out of work."
Such is the sad prospect for small family estates without heirs to step in at retirement or death.
Their debt crises are mainly a byproduct of this sad prospect, because depressed economies lead to budget deficits and deflation magnifies the burden of debt.
It is a sad prospect for a studio that used to say that it had "more stars than there are in heaven".
In the sad prospect of the compounding loss of her mother as well as her father, he asks her guardians to prepare his daughter for a great deal more than "the usual ladylike accomplishments," advising: "I should like my daughter to learn to draw, to paint and to engrave well enough to be able to earn a living without too much difficulty or repugnance.
"Well," Cruz's mother says, pausing momentarily at the sad prospect of letting her son down.
I felt sad at the prospect: Amber Shore is enchanting, infused with tradition.
Mr. Walcott said he was sad at the prospect of giving up the cottage.
Sad at the prospect that you might never see a taut, oiled, lithe young naked body again?
Whereas I previously felt sad about the prospect of getting rid of all the baby kit, I'm now palming off bits of neon plastic at every opportunity.
"There was a strong feeling from our supporters that the site should remain in the same place - many were feeling terribly sad at the prospect of it moving to another location".
Still, now that it's finally happening, I find myself oddly sad at the prospect of bisexual OKCupid becoming a thing of the past.
