What does it take to run 64-bit userland software on a 32-bit kernel?

Running 64-bit applications requires some support from the kernel: the kernel needs to at least set up page tables, interrupt tables etc. as necessary to support running 64-bit code on the CPU, and it needs to save the full 64-bit context when switching between applications (and from applications to the kernel and back). Thus a purely 32-bit kernel can’t support 64-bit userspace.

However a kernel can run 32-bit code in kernel space, while supporting 64-bit code in user space. That involves handling similar to the support required to run 32-bit applications with a 64-bit kernel: basically, the kernel has to support the 64-bit interfaces the applications expect. For example, it has to provide some mechanism for 64-bit code to call into the kernel, and preserve the meaning of the parameters (in both directions).

The question then is whether it’s worth it. On the Mac, and some other systems, a case can be made since supporting 32-bit kernel code means drivers don’t all have to make the switch simultaneously. On Linux the development model is different: anything in the kernel is migrated as necessary when large changes are made, and anything outside the kernel isn’t really supported by the kernel developers. Supporting 32-bit userland with a 64-bit kernel is certainly useful and worth the effort (at least, it was when x86-64 support was added), I’m not sure there’s a case to be made for 64-bit on 32-bit...

Snow leopard was able to run 64 bits binaries in an Intel 64 bit CPU.

It was also able to boot with a 64 bit kernel when your efi was already 64 bits (my production batch of the Macbook "transition-model" pro was already such a machine).

There was no emulation involved, you just paid a smaller performance cost when booting in 32 bits mode afair.

In pure 32-bit CPUs, you won't be able to do that, as they have no idea how to interpret 64 bit code. Unless you are emulating with software, which would be to slow for those kind of traditionally underpowered embedded class of machines.