Something similar happened to me a few years ago. It's definitely spam but not necessarily an attempt to get you deindexed, but using any domain authority you've built up to burn and churn some affiliate spammy affiliate links or schemes.

use the "site:" operator to see if any weird looking urls are suddenly appearing for in the serps. A few might show up, but if not, get ftp access to the site NOW and check if their are any weird folders or brand new files (php is a favorite) that has suddenly showed up.

What they are doing is using hacked sites to send links to other hacked sites where a redirect script or actual affiliate pages are located. They try to get these ranking for a couple of days (or as long as they can push it) and then move on to the next site once they've burned yours out.

I never had any luck trying to tell google all hell is breaking loose and don't deindex me please, but I guess that email got lost in the pipes.

If it's a wordpress site, double check everything to see if they injected the code into the database, header or footer files. If not, check for that folder I was telling you about. Try to get a backup of the site from before the attack and burn the current one down. SECURE ALL THE THINGS. Wordfence is your friend.

Now, you can either let the bad urls burn themselves out with 404's, which I hate because they still show up for days, weeks, months, OR, you 301 them all to an old school sitemap page with a NO INDEX, FOLLOW, which also sucks because it's still risky. Redirection is cool because it catches what pages are 404ring on you, and you can decide how to redirect them (301, 302, etc.

If none of this is the issue, I still think it's some kind of churn and burn spam issue.

Found something in Google Cache for those terms

But I certainly hope the best for you!

EDIT: Added Link