score:3
In my experience, travel insurance usually covers you until the date of your planned return home, or the actual date when you return home, whichever is later. This generally only applies if your delay is caused by something out of your control that is covered by your policy.
So, if you fall ill on the last day of your trip and have to be taken to hospital, your travel insurance should also cover the time you have been delayed. After all, that's what you bought it for.
I cannot recommend strongly enough that you read the fine print for your insurance policy so that you understand what it does and does not cover.
You should make sure your insurance end date is the date when you plan to actually step back into the front door of your house. Not, as you imply, the date when your flight departs from Europe.