Before my cat died he had been acting really weird for a couple of days (hiding in dark places, not eating, not purring) so I asked my brother to take him to the vet while I was at work. That afternoon I got a phone call that it appeared to be advanced cancer and the vet was recommending a couple test to rule out more benign causes, and then the recommendation was to put him to sleep. I told my boss what was going on, and took the rest of the day as a sick day. We put him to sleep that evening. She completely understood.
I was teary the next day at work, but I was there.