This article explain how to create special offer type "sold" that will hide properties from the search form, but the links to the property will be still working. This solution can be good for SEO.
1. Login to your admin panel
2. Hover Properties and click "Offer Type"
3. Add new offer type Sold with e.g. black background label and white font color
4. Check the box ""
5. Click Add New Offer Type
Now when you assign this offer type to your property it will be not displayed in the search form.