I'll go full Lovecraft on this one.
A giant self replicating fungal organism
It could be as old as the Universe itself. Plus, in some mythologies, it could be the center of the Universe, much like Azathoth. Being such an old and awesome living being, it's constantly puffing spores to every direction.
The Universe is very, very vast, but it's pretty much empty, so the probability of a spore being ejected in a direction that will make it close enough to any star is low. These spores could be ejected at low speed, so they wouldn't had time to get close to stars much further than were this being resides. On the other hand, a mysterious void in the Universe could pinpoint the location of the mother-organism.
When one of these spores get close to a star, it begins receiving energy from it in a process similar to photosynthesis. This make the spore grow in a polyp, which in turn produces more and more spores, until the star is completed surrounded. Then, the polyps mature and begin to enclose the star, closing the gaps between them until absolutely no light escapes from the star.
From an observer, outside this, it would look like the star died, because it vanished. Instead the star would be still fully operational, but 100% of its radiated energy would be absorbed by the fungal structure.
After a star is fully enclosed in this deadly embrace, it would start producing and puffing spores by itself.
This could pose a danger for the Universe, since in a few trillion years the spores could have reached a good part of the stars.
EDIT after andrey's comment. I thought about his very valid critic, and I'll enhance my suggestion.
What we perceive as dark matter and dark energy are indirect evidences of an orthogonal universe. I'm not using the work parallel here, because if another universe is totally orthogonal to ours, the mathematical projections of their dimensions onto ours would be zilch, hence we wouldn't perceive it. However, its mass and energy would affect our cosmos, hence the dark matter and dark energy.
These fungal organisms could be pandimensional beings, which exist in several different ortoghonal universes. I do understand the problem of the blackbody radiation and the source of matter for the spore-to-polyp evolution, and I propose the creature to funnel matter and energy between universes. Then, from an outside observer, the star would seem to be devoured, and there would be no blackbody radiation, since all of the absorbed energy would be funneled to another universe, in exchange for matter to grow more spores.
This way this pandimensional fungus would still conserve matter and energy, but not on a local single-cosmos-wise system. It could act as, for example, an organic Dyson sphere from an even higher civilization that learned how to control this organism. They would seed these fungus on several universes and let them evolve, so whenever the spores find a star and began their transformation into an organic Dyson sphere, they harness this energy.
I guess I went a bit too wild on this one, but I got truly excited on this idea!