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In an inelastic collision, momentum is conserved, but energy is not.
In an elastic collision, both momentum and energy are conserved.
First google the law of conservation of momentum.
In practice momentum can be lost, slide a book across the table and see for yourself.
Clearly, momentum and energy are only not conserved, if one does a superficial analysis of the system. In general, it is always "going" somewhere (energy lost goes into heating the book and table, whereas the momentum goes into moving atoms and molecules around etc.). The momentum is only lost in the superficial analysis of the book's motion because it is neither a closed nor isolated system.
So again, in practice momentum can be "lost," but this is usually because you haven't taken into account all the possible places where it could have gone (i.e. your system isn't closed and isolated).
On a more subtle note, though this may sound silly; but in EM theory the fields themselves possess energy and momentum. Therefore simplistic calculations, seemingly taking into account a whole closed and isolated system, can result in momentum or energy not being conserved, which is of course incorrect. Again though this is only because your system wasn't actually closed and isolated. You failed to take into account the momentum change in the associated field.