is there a way to figure out if there is a live incomplete sub-process of a proc

I recon that you're talking about asynchronous sub-processes.
I don't think there is a way to identify if an async sub-process is running.
You may try to pass parent process instance id in the sub-processes and during your deletion process, skip those instances.

As per my knowledge there is a plugin to get subprocesses for given process. Then you can use in conjunction with process analytics on all process report with filter of all subprocess ids and status to get active subprocesses.

Also consider using a portal report that includes sub_process_ids() data attribute to get your list of sub-processes and then checking to see if these are active.

To the best of my knowledge, the plugin as mentioned above gets the subprocesses(synchronous and synchronous) at any level whereas the sub_process_ids() gives the information about the immediate level sub-processes.

I believe we need to take a call depending on the requirement. We have come across a similar requirement and the plugin seemed best fit for us.

I think you can add some boolean value in main process which will tell you whether your subprocess is complete or not. I think that process variable you can map to your report as well. I hope this may help you in some way.

Thank you all for your input. I used sup_process_ids() to determine if there's any subprocess. luckily all of the processes I was going to delete had no sub-process so I didn't need to see if they are actually active. thank you again.