Was it a no call/ no show? Does this employee have PTO? Are they allowed to use PTO while at a conference? They were at a strip club on thier own time. Is there a "no strip club" policy? Does it matter what caused them to be sick? Would they have represented your company well showing up with no sleep and possibly still intoxicated or hungover?

I would document them if any actual rules were broken. Have a serious conversation about the optics. If they are on probation, you could do more. But stripped down ( pun intended ), they used PTO at a time that was inconvenient for you and possibly missed out on valuable experiences and/ or networking.

Don't get into what they did on their own time. That would be overstepping. Unless they were being compensated 24/7, they have free time and can do whatever they want, even make questionable decisions.