There is a website called the SCP Foundation which features a variety of creatures, objects and phenomena that border on the horrifying to the just plain weird. This one straddles the boundary between both: carnivorous blankets (or SCP-799 as its officially known on the website). Here’s the official page for it http://www.scp-wiki.net/scp-799 . If you don’t feel like reading the whole page, the blankets are basically creatures that superficially resemble ordinary blankets, coming in a variety of different shapes, colors and designs, and are described as retaining heat unusually well (of course, that’s probably their own body heat). Normally content to feed on dust, in times of extreme hunger, they are capable of becoming predatory, lying in wait for something to wrap themselves in it before eating it. They also reproduce through budding. So, the question as always is, can something like this evolve in nature?
My first thought was "it's probably some sort of fungus", and the SCP article does indeed bear out that supposition! Some sort of slime mold (which are not technically fungi, and actually span multiple taxonomic groups) could also work. The fibers of the blanket would just be fungal hyphae.
Some types of slime molds in particular are capable of metamorphosis during times of "hunger" (low food availability), which would fit this scenario. The particular metamorphosis described for SCP-799, however, is a little implausible--how do you grow a mouth on a blanket? Particularly without it being noticed? If you are content to have the creature stop actually looking like a blanket anymore when actively feeding, then I guess that's fine, but it seems unnecessary.
A more plausible approach, which could be accomplished with no metamorphosis required, would be to simply have the creature excrete toxins and digestive enzymes when wrapped around a victim. That's totally normal behavior for fungi.
The trickiest part would be evolving patterns designed to specifically trick human victims into using them as blankets. However, mimicry is a pretty darn common phenomenon in the natural world, so given an appropriate environment and evolutionary pressure, it probably could happen. I might expect such a creature to derive from an old civilization, a la the Moties from The Mote in God's Eye, where human culture has been around for so freakin' long that the entirety of the rest of the biosphere has evolved to fit into and around it. Plausible-enough starting points for the evolution of such a creature might be intentionally-engineered living blankets that end up "going feral" (so they don't need to evolve pleasing patterns--they just inherit them from their artificial, domestic ancestors, while evolving the ability to paralyze and digest large animals later), or varieties of mold that start out by, e.g., evolving to form pleasing patterns as "living wallpaper" to avoid being eradicated when humans find an infestation.
The only habitat where such an organism could develop would be a hospital. Otherwise, it would violate our understanding of population dynamics.
In a hunter-prey relationship, there are periodic undulations in population size where the hunter lags behind the prey. In the case of a man-eating blanket, prey population is zero, and stays zero, after having consumed one. Nobody wants to sleep in a bed (or under a blanket) where someone has died. Also, while technically "zero" is a stable mean value, it is not really a value that is much compatible with the notation of "population" as such.
The only place where people die regularly, and others sleep in their bed, again regularly, is a hospital.
Reproduction is another thing. Now of course, if instead of budding they reproduced e.g. with a spore cloud that infects a normal blanket, then this might actually work when there are other beds nearby (again, hospital, but also e.g. YMCA). Otherwise, the organism would have to be prepared to survive in a washing machine, which is a tough challenge to most. The budding had better be fully grown pretty fast as well, or it might land in the trash can when discovered. Darn it, who cut a blanket in half, and left it lying around here...!
My first thought when I saw this question was some form of mollusc, in the nature of a large, air breathing nudibranch or similar but the texture is all wrong, a colonial algae or a fungus might be able to take on the proper texture but I think the best option is a form of sponge. Sponges are extremely versatile and hardy creatures that already have an extremely broad existing morphological range and they already come in carnivore too.
Any type of creature we're familiar with would probably require more fluid than general room dust would give it, so it would need to induce food and drink spillages and washing cycles to stay hydrated.
There are animals using leaves as shelter from weather, and it happens that the Dionaea muscipula, or Venus fly trap, uses leaves to capture its preys.
So, start with a Dionaea with larger leaves, offering shelters to animal, and eating them from time to time.
While the trap grows bigger, the stem can slowly disappear and also the pattern on the leave can change. Now you have your new species: the Dionaea Blanketula!
To prevent that intelligent animals like humans can remember a blanket devouring their conspecific or simply refrain from using a random blanket found somewhere, I suggest the Dionaea Blanketula to stay close to places where the alcoholic content of the dwellers' blood make them prone to seek a random blanket when venturing out in the fresh air after a drink, or where the humans wouldn't be to picky about the origin of the blanket (bridges, train stations, slums, etc.).