If an object is taken from earth's surface to infinity, it's gravitational potential energy becomes zero (always taken as zero), but it doesn't make any sense as energy can never be destroyed so where did that kinetic energy go?
When the object was on the Earth's surface, its g.p.e. was negative.
When something lifted it off the surface to take it to infinity, it did work on the object, increasing its g.p.e. to 0.
If it fell from infinity toward the Earth, its g.p.e. would become negative again and it would gain kinetic energy. Likely it would subsequently heat up itself and the atmosphere as it fell
In either case, energy is conserved.
Potential energy doesn't have any physical meaning. Only potential energy difference has physical meaning. You can add a constant to the potential energy at all points, and it will not make any difference. Hence, we have the liberty to choose any point in space as the point with potential energy as 0. Choosing potential energy at infinite as 0 is most convenient for calculations. You may choose any other point to have 0 potential energy, as long as you are consistent about it.
The kinetic energy (assuming, it becomes 0 when it reaches infinity, which means the velocity is equal to escape velocity), when added to the negative potential energy near the Earth, will be equal to zero. At infinity, both the energies are zero. That is, the sum of potential and kinetic energies remain constant.