It really depends on type of "sickness".
If it's something potentially contagious like covid or a cold or D&V bug, then I'll basically not leave the house as I don't want to be responsible for anyone else catching it unnecessarily. Easier these days as I can work from home, but pre internet, I'd have had to ring in sick and have a day or two off.
I've not really had anything else bad enough to make me take a day off work. There was a short time when I got a bit of dizziness in the night, and the GP gave me some pills which he warned me I shouldn't drive when I was taking them as they cause drowsiness, so I went to work that morning (before taking the first pill) and brought a car full of work back home with me so I could work from home for the week I'd be taking the tablets.
Occasionally, I've felt a bit "off it" generally, maybe headaches or random aches and pains, but still gone to work as normal. I don't think lounging around at home feeling sorry for yourself helps much really. I'd far rather push through it and gone on with normality as I find that helps you get through it better.
My OH has managed to work throughout his chemotherapy treatment - at certain points in the treatment cycle, it wiped him out and he says he could happily just curl up and stay in bed, but he forces himself to get up and about, just takes it easy, takes a few breaks, etc., and he gets through it. He says he feels no worse getting up and on with it, than he does on the very few occasions he didn't!