If those sausages were already cooked and then sat in the fridge, the rules change a bit. Cooked sausages last 3–4 days in the fridge past the pack’s date, if stored right. That’s a decent window.
But raw sausages? That “one day” is more like a tightrope over a pit of regret. I’ve eaten them a day over and lived to tell the tale. But I’ve also had a friend who spent 12 hours full of regret after eating “almost” fresh chorizo.
So, survivor bias is real. Your anecdote isn’t data. Your gut might handle it; my gut might not. There’s no universal “yes.”