Just to give you an idea, I ran a search on Cars.com for 2009-2012 Ford Fusion and Mazda6 for $10k* or less. It returned 2,733 results, but when I limited it to 50k miles, it dropped to only 100. So meeting your budget and 50k mileage limit will be tough. But on most newer cars, expensive maintenance or repairs prior to 150k miles (if properly maintained) are very rare. *(I used $10k for my search based on the assumption that you could buy the car for closer to $9k).
The Ford Fusion and Mazda6 are two cars that seem to fit your needs very well. They're reliable (according to info here on TrueDelta as well as a few other sites) and they're actually very pleasant to drive (based on my own experience). Your best bet for low running costs will be the 2.5L 4-cylinder in either car, which is actually the same engine. The Fusion and Mazda6 share much of their basic architecture because they were designed while Ford still held controlling interest in Mazda.
If you're interested in something smaller and with slightly better fuel economy, I'd recommend the Honda Civic or Toyota Corolla (2010-2013). Both are basically indestructible and will run almost forever as long as you change the oil regularly.
As far as safety is concerned, the Fusion and Mazda6 both earn a 4-star rating from the NHTSA. The 2010-2011 Civic and 2010-2013 Corolla are rated at 3-stars, but the 2012+ Civic is 5-star rated.