Can an item be removed from Cosmos if the item cannot be read?

Intersting problem! Using SDKs it won't be possible to delete the document.

However there's a workaround. Essentially, Cosmos DB has the functionality to set Time-to-Live (TTL) property on a container/document. Once properly set at the document level, the document will be automatically deleted once the TTL expires.

However before you do that, you will need to set the TTL property on the container to "On" (default is Off). What this setting mean is that documents in the container will automatically delete if TTL is specified on the document and once the TTL has expired. This you can set through Data Explorer in Azure Portal as shown below.

Once the TTL is configured properly on the container level, next thing you would need to do is update the document and set the TTL property on the document. You can do so by using Cosmos DB SDK. Please see sample code where I had set the TTL to be 30 seconds (you can set it as low as 1 second). Once the upsert operation succeeds, you will see the document gets automatically deleted after TTL has expired on the document (30 seconds in my case).

    static async Task UpdateItemTtl()
    {
        CosmosClient cosmosClient = new CosmosClient(connectionString);
        Container container = cosmosClient.GetContainer(databaseName, containerName);
        string documentBody = "{\"ttl\": 30, \"Code\": \"https://CokeURL.com/gbm330\", \"Quantity\": 1, \"ActivityId\": \"0000\", \"id\": \"https://CokeURL.com/gbm330\"}";
        Object o = JsonConvert.DeserializeObject(documentBody);
        ItemResponse<object> response = await container.UpsertItemAsync(o, new PartitionKey("0000"));
        documentBody = JsonConvert.SerializeObject(response.Resource);
        Console.WriteLine(documentBody);
    }