is this sentence correct?

They are a fact.

You could concoct a scenario where it makes sense – some weird distributed system that, when taken as a whole, is equivalent to a “fact”, but the plural/singular disagreement is too strong for me to ever call it correct.

“Black holes are not mere science fiction. They are a fact.”

The alternate “They are facts.” doesn’t seem to work. After giving it more thought, removing the “a” would be am improvement.

I could think of a context where it might be acceptable:

Vampires are not just characters in scary movies. They are a fact of life in Transylvania.

But you’d have to be very careful. The following would not be acceptable:

Two plus two equals four and four plus four equals eight. They are a fact of arithmetic.

(Which is a lot like what panache45 just said.)

In this case, I think you’re talking about an ellipsis. A more complete version of the example sentence would include “the existence of”. If it’s included, you go to a singular subject/singular linking verb/singular predicate nominative with complete agreement. If you don’t include it, then you revert to plural subject/plural linking verb/singular predicate nominativewith an apparent, though understood, disagreement.

And part of it may be the choice of predicate nominative. If you say “they are a team”, no one finds that awkward.