Can a child retain the same Apple ID when they grow up and leave Family Sharing?

Yes, it's only child accounts that have to remain within a family share, when they are over-13 (age varies by country) they can leave the family and keep their account : Leave Family Sharing - Apple Support

Any family member over the age of 13 can remove themselves from a family group at any time.*

• In iOS 8 or later, tap Settings > iCloud > Family, tap your name, then tap Leave Family.
• In OS X Yosemite or later, go to Apple menu > System Preferences > iCloud > Manage Family, click your name, then click the Remove ➖ button in the bottom-left corner.

When you turn off Family Sharing, you leave the family. After you leave a family, you can join or set up a new one. However you can only switch to a different family group once per year.

I understand that there would probably be a loss of acquired content but can the Apple ID live on?

There is no loss of content.

All content purchased from the iTunes Store stays permanently with the account from which it was purchased. (Whether a 25 year old still wants to listen to the songs they bought at age 6 is another question, ha, ha, but iTunes certainly will allow it).

Yes, the child will still be able to use their Apple ID after they are 13 years old. When an account is setup for them parental controls are automatically set up as well. They will also be apart of the family sharing until they have left, or until they are removed by the "Organizer".