Physics question about collisions with conservation of momentum and energy.?

There is no such thing as a "stationary" object. If the bullet embeds itself into the wooden wall of a house, the momentum of the bullet, house, and the entire planet earth must be the same before the collision as after. Almost all the kinetic energy of the bullet will go into heat, noise, and deformation of the house, but the bullet will have some kinetic energy afterward as it moves with the house and the earth.