<snip> When I add a DC X'0000' and I force a SOC1, I don't see any dump added to IPCS. </snip> If your program has a SYSMDUMP DD statement and your program ends with an operation exception, you will get a SYSMDUMP. Where you have targeted that SYSMDUMP is up to you. It is up to you to tell IPCS what dump you are looking at.
Within IPCS, "browse" is a way to look at storage, or the "L" (list) command. "IPCS STATUS FAILDATA" is a good place to start. For the cases described, SDUMP is not appropriate (even if you're allowed to do so). Peter Relson z/OS Core Technology Design