Is there a possibility that recent high tensions between moderators and Stack Exchange managers will result in the shutdown of a number of Stack Exchange sites?
We can't know this for sure, but IMHO it's not likely.
In the past, sites have only been shut down because there were not enough people willing to moderate the site. Yes, some smaller sites have lost one or more moderators, and Stack Exchange generally strives to have at least three moderators per site. But it's likely that at some point, when this mess has settled down, they'll either organize pro-tempore elections on those sites or just appoint new users willing to moderate.
I don't expect Stack Overflow Inc. to shutdown certain sites as a sort of punishment; why would a community be punished because of an argument with a few elected people on those sites? (Who might have the support of a much larger group on that site, sure.) But then, I didn't expect them to fire a particular moderator the way they did either.
The Workplace was left without active moderators for a week.
The high rep users and the Community Moderation team stepped up to cover the gaps during that period.
There’s no reason why this can’t continue until elections are held for the relevant site.