Power Query - Prevent complete dataset to be refreshed when there's something wrong with the source

Sure. You would need to do a row count on the source table. Then if it has 0 records, return an error. That will halt the query refresh.

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMlTSAeJYnWglIyDLGMwyBrJMlGJjAQ==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Column1 = _t, Column2 = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Column1", Int64.Type}, {"Column2", Int64.Type}}),
    IsValidData =
        if Table.RowCount(#"Changed Type") = 3
            then
                error [ 
                    Reason = "SourceTableEmpty", 
                    Message = "Source table has no records", 
                    Detail = "Database.TableName" 
                ]
        else #"Changed Type"
in
    IsValidData

In this example, I tested for 3 records so it would error out. But use 0 in your actual use case. It will return that error to the service.

How to use M code provided in a blank query:
1) In Power Query, select New Source, then Blank Query
2) On the Home ribbon, select "Advanced Editor" button
3) Remove everything you see, then paste the M code I've given you in that box.
4) Press Done
5) See this article if you need help using this M code in your model.