Question
Statement $-1$: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement $-2$ : Principle of conservation of momentum holds true for all kinds of collisions.

Answer

In completely inelastic collision, all energy is not lost(so,  tatement $-1$ is true) and the principle of conservation of momentum holds good for all kinds of collisions (so, statement $-2$ is true) . Statement $-2$ explains statement $-1$ correctly because applying the principle of conservation of momentum, we can get the common velocity and hence the kinetic energy of the combined body. 

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