As of February 2018, support for 32-bit x86 hardware has been removed from illumos. This only affects the kernel; 32-bit applications are still supported.
In practice, 32-bit hardware support hasn't been well-tested for a while, and most illumos distributions haven't supported 32-bit hardware for a while.
However, you can still run older Tribblix on 32-bit hardware, with certain caveats.
The best base release to download and run is the original 0m20 release. The update releases may be problematic, as will the omnitribblix variant. Note that all the 0m20 updates, and the 0m20 omnitribblix variant, share the same application repository - there is no difference in terms of what applications are available, it's just the kernel that differs between the various releases in the 0m20 series. If you're running on 32-bit hardware, do not upgrade to any of the update releases or any later version such as 0m21.
WIth 32-bit hardware, you're often looking at hardware that is resource constrained in other ways. Tribblix is the best illumos distribution for such resource constrained systems, allowing a more minimal install, and supporting installation to ufs rather than zfs. (If you have less than 1G of RAM, ufs is recommended, and should be comfortable on even a 512M system.)
Note that while Tribblix is happy to allow for 32-bit hardware, some modern applications may be aimed at 64-bit hardware. For example, golang is only available for 64-bit illumos, as will be any applications written in Go. Java 8 is 64-bit only, so you're limited to Java 7. Many new languages, runtimes, and applications, will only be 64-bit.