Software is either in support, or it isn't. I will not support software the source vendor will not support. The user can either upgrade, or replace it with one of the many free options. Any process otherwise exposes me to liability.
It only exposes you to liability if you touch it or are the responsible party for maintaining it.
And if a client adamantly insists they want to keep it, then they need to sign something that says they've been warned about the potential perils of unpatched software.
I worry very little about Office in general, as I cannot count the number of clients I've had who continue to use out-of-support versions without issue. However, some use Outlook and some don't.
If this is a residential customer for whom you're doing service, and you've recommended they update and told them why, you've covered yourself provided you can prove that if disaster strikes. Unlike
@Sky-Knight, I'm disinclined to believe that disaster will be likely, let alone imminent, if this is a user who's not been inclined to get infections to begin with.
I have a lot of clients, though certainly not all of them, who could likely use Windows XP and Office 2003 and be connected to the internet for years and never have an issue. I don't recommend or support that, but in the end the vast majority of infectious vectors are invited in by direct user action. It's a very small percentage that wheedle their way on to a system completely uninvited. Users have always been the weakest link in the security chain, and the ones that haven't had an antivirus detect something in years and years are very likely to have that situation continue, because it's a direct result of having developed the habits necessary for safe interaction with cyberspace.
Then there are other clients of mine that, if I had not larded their machines with certain software that is meant to protect them from themselves, they'd be having major crash and burns on a weekly basis, even using the latest of absolutely everything.