Daughter.1 can't find her laptop. She's searched the whole flat, a few times, and it's missing. She can only suspect that a guest might have walked off with it. It's a problem, for several reasons.
Your browser remembers where you've been, unless you tell it to forget. It also remembers your passwords, a handy feature. So now she has to go onto everything she uses, and change her passwords. I also suggested that she check her bank and card statements carefully for a while, just in case.
She hasn't lost any data, because she didn't keep data on it. But it shows you the importance of backups - it isn't only the possibility of a disk crashing, it's also the possibility of losing your computer, either by forgetfulness, or theft.
She asked me if it could be traced. No, it can't.
Here's how things work. When your computer contacts your ISP to get onto the internet, your ISP gives it a temporary loan of an IP address, which looks like 220.127.116.11. The ISP has a record of the date and time that this happened, and it knows which customer it's dealing with.
So if the user of that computer were to download a copyrighted file, and if the aggrieved company got a court order and knew when the download happened and from where, it could request that the ISP look up its logs to fnid out which customer had the IP address that downloaded the file at the time it happened, and so they can take legal action against the downloader, because now they have the customer's name and address.
A defence sometimes used, is that it wasn't the customer, it was someone else using that computer. That might, or might not, work.
The police can go the same route, and find out the name and address of the customer who is suspected of doing something illegal online.
Unfortunately, that doesn't help daughter.1, because if her computer was stolen and is being used, it won't be using her ISP, because the computer doesn't have the password for the ISP, the router does that.
... later ...
She found the laptop!