what is the trigger point for this output type(manual, automatic or event based), you can ask the developer to put a check in the output program for the custom field before execution which can control the trigger of output
Once the custom field (lets call Block) is removed .. delivery outputs should work as per SAP stanadrd. ----Do you expect system to keep checking this field and if this is removed by user then a automatic output should get triggered, if yes then you need to define a batch job with your custom program if no then someone has to manually trigger this.