"closed relatives" is a correct and usable phrase in written English.
It is commonly used to refer to family members who have formed a tight bond, such as a family group that is close and maintains frequent contact. For example, "My immediate family are my closest and most important closed relatives."
Exact(1)
As the service closed, relatives walked slowly back to their pickups.
Similar(59)
Send invitations to close relatives and friends only.
"They are our closest relatives".
Mrs. Clark left no close relatives.
They focussed on chimpanzees, our closest relatives.
Close relatives include crabs, crayfish, and lobsters.
And transparency and liquidity are close relatives.
"They are not close relatives".
He leaves no close relatives.
Many for example point our closest relatives.
Its closest relatives live in West Africa.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com