Default Property Status field can show in search options, but in Advanced Search custom fields it is considered a text field. You must use Compare “LIKE” and then in search user needs to “type” the exact property name status as it is written by admin.
If you need a dropdown in search – I can suggest this:
a. Create a new dropdown custom field for status
b. When you create a property you select status for the colored labeled and status for dropdown c. use in search the dropdown