I don't think Macs are less safe today than 10 years ago, however, using an outdated OS is unsafe. You can get an used and decent Mac for less than $200. The good thing about Mac OS is that is so good you don't really need to have the latest model to do your everyday stuff in it.

A couple of years ago (like 8-9 years or so) my mom's desktop PC was struggling with Windows, possible malware and viruses. With no money or intentions of upgrading the hardware or buying a new one, there was no real reason either to reformat and reinstall Windows, so I installed Ubuntu 9.10. She was really happy, the performance was awesome and she was able to do her stuff without any slowdowns (Internet browsing, word processing, printing, facebook and youtube). Then the computer broke, maybe the motherboard I didn't care, I found a good deal on an used mac mini for her and she moved. She's been a Mac user since 2012, always using low end devices without any issues. She likes the stuff because it just works and that's what matters most.

If your mom's computer usage is limited to basic stuff such as internet browsing and word processing there's no reason not to have her move to Linux. It's free, stable, secure. It won't slow down after a couple of weeks and will take full advantage of the hardware.