Depends on the person, and depends your definition of out of shape. For me, if I take 3 days off I feel terrible on runs for about 5 days. If I take a week off it takes a couple weeks to get back to feeling like I could pop off a 5k within 30 seconds of my PR. A few months ago, after a race I'd trained for for 3 months, I ran an average of once every 2 days for a month, and during that time I ate like crap (gained almost 15 pounds) and was generally a lazy slob. It took a couple weeks of normal running (got back to normal weight) before I felt like I was "kinda in shape"--which to me means 2 weeks away from running a race and not being too embarrassed about it.
In general? A week can leave you feeling stale, but after a season it might be necessary. Someone doesn't "lose" their running shape or endurance, they just get farther away from being able to access it.