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.
Note
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.
Anyway, deleted contact will not show in the search results or the contact list.