It depends on the vehicle but I have always kept either an inexpensive rectangular bag or microfiber fleece blanket, depending on the seasons, that blended in with the car's interior.

Hatchback / SUV:
Unzipped the bag and used it as a blanket to cover the cargo area. A quick glance inside and it looks like the rug. I have stored small odds and ends under the bag / blanket and kept things hidden. Putting groceries and such on top of the bag / blanket has never damaged them.
I will sometimes drape a blanket over the back seat which keeps it handy and protects the seat from dogs or messy passengers.

Cars with a trunk:
If the car has fold down rear seats I'll drape it as above. If not I'll just put it in an extra big stuff sack or fold it loose in the trunk. As long as it's not too compressed you should be fine.

Either way I'll take it out once a month or so and shake it. I've been doing this for many years and haven't had a problem with loft. Dark colors have faded in the SUV but it took a few years.