Would it be possible to design a tiny satellite, such as a femtosatellite or a chipsat, with such a shape and ballistic coefficient, that it would survive reentry without a heat shield? A bit like this feathery question except that our chipsat wouldn't be made of quite the same material. Somewhat of the opposite of this question.
A correctly prepared (shielded) nanosat could survive the reentry.
A satellite the scale of cubesat around Kármán Line would experience about 1 kilowatt of heating. This is not what a cubesat electronics can survive - but this is something a layer of aerogel can stop from conducting in, a mirror-coated foil from radiating in, and a few centimeters of light ablator to dissipate for a couple minutes. So if you package your femtosat of, say, 10cm^3 in a cubesat form factor (1000cm^3) of lightweight thermal shielding, it should survive just fine.
Locating it on the ground after reentry is an entirely different matter...
I think it's an interesting question, The way I see it is your satellite stays in orbit because of it's high speed but it also burns up because of it's high speed. If you can get it traveling slow enough by the time it reaches the atmosphere you should be able to use atmospheric drag without burning up. So you would need a way to slow it between the orbit height and speed and the atmosphere.
I think it could be interesting do the math for trying to slow a chipsat by using a collection of tethers using drag generated by geomagnetically induced current, so using the magnetic field of the earth to slow down before hitting the atmosphere. But I wouldn't know where to begin with running those sorts of calculations.