That pack nut is looking pretty good there. Reminds me of a consult I had with my proctologist after my divorce.
Yeah, Terry's spot on; you need to get a grip on the stem with the right tool, and back it out of there. The tile people aren't plumbing people, so you may have to enlarge the hole a bit to allow the socket to go in there and grab the stem so that it can be removed. Chip the tile away carefully with a hammer and your least favorite screwdriver in small increments until the socket fits down in the wall. When you get the right socket on the right spot, try to unscrew it CCW. When it becomes abundantly clear that you're about to round it off, stop and try it the other way, as absurd as it may seem. Then try it CCW again.
I hate to revisit this, but last time I had a problem removing a stem, I had to go purchase a 15/16 deep well socket, saw off the stem so the socket wouldn't bottom out, and take my 18" 1/2" breaker bar out of my van that I use for my lug wrench. Worked like magic.
Getting in a hurry pretty much guarantees failure.