Brakes loose, cable hanging out

The inner cable is very rusty. I would think that the cable friction is so great that the spring of the brake cannot pull back against it. Maybe at the other end of the cable, something has popped out of place, you can inspect the other end and see if this is the case.

Ultimately, the solution is going to be to fit, or to have fitted, new cables and the brakes setting up again to work well. If that cable condition is indicative of the rest of the bike, a good service is due which will make it nicer and safer to ride.

There are several things that can lead to this:

1. either the cable tube has moved along the steel cable, which means it has popped out of the connector at the other end

2. or the length of cable and tube are not matching any more - either because the cable tube has broken, or more likely the steel cable is broken inside.

3. The cable may have pulled through the clamp screw at the brake. In this case open the clamp screw, tighten the cable and close the clamp screw again.

Even if it's just popped out, I recommend changing at least the inner steel cable, especially since brakes are safety relevant. Very likely, the brake hose is also worn & rusty, and exchanging that as well would give you a brake that operates a lot more smoothly and doesn't require as much force in your hands.

I'd also grease the new cables, but that may depend on the model if that's advised, some cables may already be coated to reduce friction without grease.