Do Unisys latest mainframe systems still use ones' complement representations?

Yes, the 2200 line still uses ones complement. Emulating one's complement on a two's complement machine is not hard, you just need to add the carry back in (end around carry). And the MCP line still uses signed magnitude.

I don't know the facts.

What I do know is that when you have mountains of running software, it is really hard to pull the technology base out from underneath.

I'd make a pretty big bet that it still does ones' complement math in any instruction set simulation (or chip implementation) that runs the software.

You can build an emulator on top of any other CPU. UNISYS asked us to help them do that back around 2007 with an explicit target of a hi-reliability 64 CPU x86 system. Then there was a financial crisis so the project didn't materialize for us.

They've obviously done a great deal of engineering since to keep it alive. And yes, people still run these.