Sebastian
Tho your insect is a little smashed it is a photo of an assassin bug. I believe it is a Masked hunter not the Corsair bug...they do look similar from a photo.
The Masked hunter adult is in the true bug order and has piercing sucking mouthparts. These insects feed on other insects...tho they can 'bite' humans if mishandled. The masked hunters are known for feeding on bed bugs...so I hope you do not have those? The adults and nymphs do feed on a wide variety of other insects. The nymphs are seen covered with dust, lint, sand and other such debris. Here is another photo of the nymph on the Insect ID site - http://www.simplegiftsfarm.com/white-furry-beetle-or-spider-nymph-of-masked-hunter-bug-comments.html
The adults are known to come to lights so that is another way it could have gotten in your house.
These are beneficial insects, so perhaps next time (if you are awake enough) put it outside rather than killing it! :-)