Contacts may be archived, so they do not show in the contact list or the search results.
How to delete a contact
Step 1 - Access the contact list by clicking on the "Contacts" menu.
Step 2 - Display the contact details by clicking on their name from the search results or the contact list.
Step 3 - Click the "Edit" button.
Step 4 - Click the "Delete" button located at the bottom left-hand corner of the page.
If the contact you have deleted is still attached to valid quotes or invoices, their profile will remain accessible from these documents. A note saying the contact was archived will show on the contact description. You can also unarchived this contact anytime.
Anyway, deleted contact will not show in the search results or the contact list.