How can electrons be absorbed by material of the object in TEM microscope?

In Transmission Electron Microscope (TEM), the electron bean behaves as waves, i.e. it exhibits the wave nature of particles. The beam undergoes transmission and absorption (as well as other wave natures like diffraction and reflection) when it passes through matter.

The "absorption" of electron doesn't mean that the electron itself is being absorbed. "Absorption of electron" means all the kinetic energy of the electron is lost and the energy is transferred to the target atom.