But they didn't block the desert, only air zone and also only directly above the city not beyond it.

That's kind of what I'm thinking too though my money would be on something like "super secret stealth cruise missile ripped off it's mounting pylon" or control software went crazy rather than an airframe loss.

It's likely be something small enough and with little/no fuel because if it left a big smoking hole they'd find it quick. And it's gotta be something with fairly questionable aerodynamic properties (i.e. damaged) or questionable guidance (i.e not an inadvertently released bomb) otherwise they'd have a very good idea of where it landed.