The "On Market" option belongs to each individual property.
This setting determines whether or not the property will be included in the search results.
When "editing" the property, you'll see in under the "Marketing" tab.
Every time an import runs, the Import add-on makes an API call - this call picks up all the properties that are included in the import feed. Each property will have its own ID in the feed to represent it.
Every time a new import runs, it registers as an "event" into an "import record" and provides us with an individual import log (named by a time stamps & date) that marks that event, found in the Active Automatic Imports > “Logs”.
Each import "event" carries itself a list of properties and their IDs:
You can use the the "Post ID" to track if a property is still being received in the import feed.
When an import event is running, it goes through a current list of property IDs that are being "sent through, in the feed".
It then compares that current list of Property IDs to the list found in the most recent import event that was registered in the import record.
Those two lists (current list of Property IDs in the feed vs most recent list of Property IDs - taken from the most recent registered import event), get compared.
During that comparison, if the number of IDs in the current list is smaller and missing a few property IDs, then the Import add-on will assume that those missing IDs are properties that are no longer being received through the feed. As a consequence, it will untick the "On Market" option on all the properties it determined as "no longer being received through the feed".