Question

A large mass collides with a stationary, smaller mass. How will the masses behave if the collision is inelastic?

Answer 1

Well you can derive the results using momentum conservation & few results from
coefficient of restitution "e" equation then using proper approximations.

If collision is perfectly inelastic then Larger mass has no change of momentum
& smaller mass sticks with larger mass and system translates with velocity of larger mass
which was before the collision ( Under condition that masses are spherical in shape & larger mass is
far more heavier than the smaller mass)

Answer 2

In a purely inelastic collision, the smaller mass would just go along with the larger mass. There will be change in momentum of the larger mass indeed.
M*u = (M + m)*v where u is initial velocity of larger mass, and v is the final velocity of the 2-body system.

if M >> m, then v is approximately equal to u