Personally, I've had mixed results. I think there are two key factors. One is the content of the site the search engine has previously indexed. The other is the domain ownership information. I believe ...
If the content/site stays the same, and the domain registration information changes the answer is a "maybe"
If the content/site changes, and the domain registration information changes the answer is "no". I'm not positive regarding this, but this is my impression based on my own experiences.
If the content/site stays the same and domain registration information stays the same ... then a clear yes.
In your scenario, it is worthwhile maybe if the site does not
change "significantly". But I wouldn't expect a new site with new domain registration information to carry forward the previous authority of an old site like you describe.
The above is very focused on search engines, there may be benefits to owning the domain outside of the search engines. It is hard to tell the traffic established outside of search engines until you own it and get it setup with stats, etc. One consideration I often have, is this worth it in comparison to a brand new domain. If it is 10 years old, why did someone let it go. Is it penalized? Not infrequent when old domains are let go. Or are there truly benefits to the domain's links/referrals being received. Some times a new domain is better, compared to a penalized domain associated with bad neighborhoods. Some times an expired domain is better, regardless of search engines, if it is well established with quality listings, etc.
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