This is a tough one. As measured by crash tests, cars have gotten much safer over the past decade. Less clear is how much the newer crash tests, which cars tended to fail until they were redesigned to pass them, reflect real-world safety. How much less likely are you to be injured (or worse) in the newer cars designed to pass the latest crash tests? I don't know.
I say all this because it's going to hard to to find an even somewhat reliable car for $3,800 that does well on the lastest crash tests.
Your best bet could be a 2005-2007 Ford Five Hundred SEL with front-wheel drive and the optional side air bags. I wouldn't get the SE base trim or all-drive to avoid the CVT transmission. The FWD SEL and Limited used a conventional six-speed automatic manufactured by a Toyota affliate. Plus the AWD system has its own weak points.
The Five Hundred is very roomy and among the safest somewhat affordable cars of its time period. Reliability has been good if not great in our survey. I'd have any car this age thoroughly inspected by a mechanic familar with the model.