I don't know what model as there was nothing to identify it and no one to ask but it looks like one of their 250s or 300s.
It has milestones proudly displayed. Yes, there's a railing in the way. I suspected the owner might be put out if I moved it for photographic purposes.
The 250,000 km was allegedly achieved at Zschopau (corrected spelling) where it was made. 150,000 km was reached at Vladimir, near Moscow, if I read the Cyrillic correctly.
How true this is is anybody's guess as the thought of going that distance on a single cylinder bike powered by an example of the Spawn of Satan seems quite a challenge.
MZ were an East German bike maker who grew out of DKW, a subsidiary of Auto Union which decamped to the West after the war leaving their remaining assets behind. Like most of East Germany's industry MZ thrived with a captive audience and declined after reunification and privatisation. They stopped trading in 2008. There was an attempt to revive the brand but that failed too.
No, I have no idea why Zschopau is spelled the way it is or how it's pronounced although I'd guess Tschopau.