Brene Brown talks about vulnerability and leadership in her TED talk: https://www.ted.com/talks/brene_brown_on_vulnerability

Her book describes research on leaders who discuss their vulnerabilities with their teams. The outcomes included more motivated staff, more self-directed managemement, and better normalization of risk-taking, e.g. the famous startup mantra "move fast and break things".

Quick summary here: https://www.scottsmarketplace.com/blog/business/brene-brown/