The system requirements for future Debian i386 releases has been changed to 686-class processors

Last year it was decided to increase the minimum CPU features for the
i386 architecture to 686-class in the stretch release cycle.  This
means dropping support for 586-class and hybrid 586/686
processors[1].(Support for 486-class processors was dropped, somewhat
accidentally, in squeeze.)

This was implemented in the Linux kernel packages starting with Linux
4.3, which was uploaded to unstable in December last year.

In case you missed that change, gcc for i386 has recently been changed
to target 686-class processors and is generating code that will crash
on other processors.  Any such systems still running testing or
unstable will need to be switched to run stable (jessie).

The older processors will continue to be supported in jessie until at
least 2018, and until 2020 if i386 is included in jessie LTS.

[1] The following processors, supported in jessie, are now unspported:

* AMD K5, K6, K6-2 (aka K6 3D), K6-3
* DM&P/SiS Vortex86, Vortex86SX
* Cyrix III, MediaGX, MediaGXm
* IDT Winchip C6, Winchip 2
* Intel Pentium, Pentium with MMX
* Rise mP6
* VIA C3 'Samuel 2', C3 'Ezra'

Ben.