Here is what I've found going back to 1990-91, coaches that won zero or 1 conference games.
0-18 Bill Foster NW returned
0-16 Kevin O'Neill NW let go
1-15 Jim O'Brien OSU returned
1-15 Ed DeChellis PSU returned
1-17 Ricky Byrdsong (RIP) NW returned
1-17 Bill Carmody NW returned
1-17 Tom Crean Indiana returned
1-17 Eddie Jordan Rutgers let go
Obviously Northwestern is a unique example, and Crean was in his first year after Indiana imploded the year previous. Jim O'Brien made up for it by cheating. But overall, it's been way more likely to return after a year like that then be fired. And we aren't going to go 1-17 or 0-18 anyway IMO, should win at least four somewhere in there. If I missed anyone feel free to correct me.