After the massive, famous battles that occured along the Eastern front, what would be done with the smoldering ruins of the tanks? The knocked out or still functioning artillery pieces? And the hundreds of thousands - if not millions - of Wehrmacht/Red Army bodies?
Its a common misconception that a 'destroyed' tank is somehow beyond repair - both sides had sophisticated Battlefield recovery initiatives that allowed for destroyed and knocked out vehicles to be recovered, repaired, or scrapped if necessary. Bodies are another issue, and there is much evidence that bodies were left to freeze in the Steppe winters or rot in the equally unforgiving Steppe summers. Generally speaking, bodies would be collected at the end of an active advance or conclusion of a successful defense, and either buried on field, or theoritically sent for repatriation. The rapid rates of advance and generally high-tempo of operations often precluded the latter, and many RKKA and Heer bodies were buried with little ceremony near where they died (Hence why many monuments often have the recorded names of the dead, acting almost as a collective tombstone in some instances) Often the only evidence we have of a soldier being killed in action are reports and identification tags. Therefore, I hope those who read the answer allow me a generalization: Recovery and care of bodies, in a war of maneuver, generally degenerates as combat becomes more fluid and hectic.
It is still not uncommon, all these years later, for construction efforts and local amateurs to stumble across skeletal remains, and I believe in 2012 (EDIT: 2000) a relatively intact T-34 was recovered from the bottom of a river in Poland.
Captured artillery pieces would, especially in the German case, inevitably be pressed into effective service. The same will be said of Small-Arms; this was so true for several variants of submachineguns and rifles that the Germans gave them Heer model designations and often added them to tables of organization.
EDIT: I added about 12 years to the time line, here's one of various examples of the dregs of war being found in odd locations: https://www.youtube.com/watch?v=YNJ-acc9Qsk
Here's an article from English Russia (I know, I know...) here on either a similar or the same instance: http://englishrussia.com/2006/09/17/russian-tank-recovered-from-the-lake-after-50-years-been-there/