Which parameters was a stored procedure or command executed with?
If you have a suspicion about which processes/procedures, etc cause the issue, could you not use SQL Profiler / Trace / extended events to get the data? - it is then fully recorded including the Parameters that were passed. - of course this would need to be running ahead of time - not any use once it's already running. However a well filtered Trace can have relatively low performance impact, so you could leave the Trace running all the time.

Here's basic how to setup a Trace/Profiler: How To Create a Trace with SQL Server Profiler

You can find better sources of info on this once you have your head round the concepts.