At least in the case of Auditors and/or Assessors who can't get out tax bills on time, the bill proposed by Rep Ed Soliday (R) would allow the county commissioners and council by 2/3 vote to remove them.
He does go on in the article in the Chesterton Tribune to suggest that due to the limited time for the session this year, and the amount of other issues facing the legislature, that this bill may not proceed far.
Although I agree that more accountability is necessary, I have often thought that Assessors and Auditors and perhaps even Treasurers should not be elected anyway. What ever happened to the proposals that were floating around to merge those three financial positions in a county into an employed role? Create the position of County Financial Officer, which could then have all three salaries to go out and hire top notch talent, and fire that person if they can't perform.
It seems so many bandaids are being suggested for these "skill" positions over the last couple years, but what about thinking about reforming the whole process so it makes sense. Joe Q Public couldn't even tell you what the Auditor or Treasurer do. And we all know assessing is a skill position, when those skills are missing things can go awry.