Techincally, there is only one way for the aircraft to remain hanging motionless in the air: if weight and lift cancel each other out perfectly, and at the same time thrust and drag cancel each other out too. But this is incredibly rare. To stay in the air and sustain its flight, an aircraft needs to be moving forward.

If by "without running" you mean without engine power, the answer is yes, a plane can fly (glide) for a significant distance, but it cannot maintain altitude indefinitely. Every fixed-wing aircraft has a "glide ratio." For a typical commercial airliner like a Boeing 737, the ratio is roughly 15:1, meaning for every mile of altitude it loses, it can travel 15 miles forward. This was famously demonstrated by the "Miracle on the Hudson" and the "Gimli Glider" incident. If the engines fail, the wings still generate lift as long as the aircraft maintains sufficient forward airspeed by "trading" its altitude for speed. The pilot must pitch the nose down to maintain that speed. Without engines, the plane becomes a very heavy glider. It can be steered and landed safely, but the pilot only has one chance to get the landing right, as there is no power to "go around" for a second attempt. This is why pilots are rigorously trained in "dead-stick" landing procedures during their certification.