I have never hear of what you describe, but it must be that when you registered the domain, the old name servers are still listed for the domain.
If your domain expires, then your site that you have hosted cannot be seen any longer. When the domain is active, visitors that want to see the domain are make a hidden request for the server to the DNS record that lists where the name servers are. The name servers then tell where the site is hosted. (Sorry if this is confusing, I may not be explaining it as well as I could.)
But the main thing is that any site that is hosted is not directly affected when the domain expires, you just can't get to it using the domain.
If the domain is later registered and it has the same name servers listed, the site will then "reappear".
You can leave it like this before you are ready to host your own site, contact the person that owns the site you are seeing and ask if they want to buy the domain from you, or just change the name servers to something else.
It's a sad but true fact that many domains expire all the time and the owner does not know. They later lose the domain and someone else is able to buy it. You can help guard against this by ALWAYS having a different email address for each contact in your domain name. This way if one address does not work, another should and you will get the message to renew your domain before you lose it.
Update:The OP can do what they want including leaving the existing name servers. If it were me, I would contact the old web site owner and let them know what happened, that they have lost the domain. Offering to sell it to the old owner is a real possibility, but I doubt the OP wants to do that since they bought the domain for a friend. If the new domain owner wanted to be nice they could leave the domain pointing to the old site with the understanding that the old owner would have to get a new domain and put their site on it after which the domain could point whereever the OP wanted.
Or the domain could have a site that tells people where to find different people that all share the same name. It would be a "vertical directory" much like what we have done with our MatsumotoPhotography.com domain. We made a directory that only has listings of photographers whose last name is Matsumoto.