Confusion regarding centrifugal force

If we observe it from a frame of reference of the ring , since ring is rotating the particle must experience a centrifugal force and hence it will fly off .

But from space frame, it doesn't.

Why does this happens ?

The centrifugal force is not the only inertial force in a rotating reference frame. You are neglecting the Coriolis force. The Coriolis force is given by $$ -2 m (vec omega times vec v) $$ where $vec omega$ is the angular velocity of the rotating reference frame relative to the inertial frame and $vec v$ is the velocity in the rotating frame.

Note that your particle has a velocity of $vec v = -vec omega times vec r$. This is in the opposite direction as the centrifugal force and is twice the magnitude. So the total inertial force is centripetal and the particle undergoes uniform circular motion in the rotating frame, as expected.

It is not necessary for a particle to be in contact with anything to experience the inertial forces. They apply to all objects in the frame.