This statement is as old as psychology and has been asked online many times. The answer to this question has been sought even by scientists and philosophers but no answer has been agreed upon by all, it now remains any ones opinion and theories.
Nevertheless, assuming there existed such a force and such an object and the two forces set against each other colliding they would pass through each other since none will concede to each other. The force will pass through the immovable object the object will remain steady and standing. None would be affected by each other.
“What will happen when an immovable object meets an unstoppable forces?” is a physiological question. If you look at it carefully the two states of the force and objects is something of impossibility. There can never exist the two forces. One will always cancel each other in a practical world.
An object so big that it cannot move is a fallacy in this physical world we live in. The planets we live in is in constant mobility, the Earth itself moves, and so another thing in and on it moves too. Scientist has proved that the entire universe is moving away or around something and nothing is stationary. So practically speaking nothing is immovable.