Closed contact showing on the list

Hi,

I noticed something,
We wanted to close a contact because we will not use him anymore, but he did tickets in the past and we want to keep this history, so we're not deleting him.
But when closing the given contact, he continues to be shown in the "contact drop down list" when for example creating a new ticket and selecting the project he is affected (there are other contacts).

What can we do to avoid this ?

Thank you,

Regards