Which professions can't avail of bankruptcy or insolvency?

The poster in this thread says that she cannot avail of personal insolvency because she is a pharmacist.
Moving on with negative equity

I find that very strange. Why would being insolvent affect one's role as a pharmacist?

But on a broader issue which professions can't avail of insolvency in case they lose their job?

Solicitor?
Auditor?
Barrister?
A senior position in...

Which professions can't avail of bankruptcy or insolvency?