I assume management gets both annual bonus and equity as a part of their compensation, so I would argue that yes, management is sharing in the loss, in particular with the equity.
Yeah. Management work for the owners just like everybody else. They're workers who happen to not be represented by the union.
Management only takes losses so far as they have equity stakes in the company, which is to say the extent to which they are owners. When GM lost $38 billion in a year the people who own the company took that hit.
That's why employees usually don't value ownership in a company, because it cuts both ways. A salary only deposits into your account.