Not sure I agree that every business needs 6 months of expenses, but what you do is let them fail, or raise capital from investors on terms that may not be so favorable to them (would dilute existing shareholders).
This would incentivize future companies to operate a bit more conservatively. The pattern of corporate irresponsibility followed by taxpayer-funded bailouts is a moral hazard.
The employees should get unemployment benefits. We should take some of the money we use for corporate welfare and shift it to individual welfare until jobs come back.
On your second point, no we should not. Do you think it's hypocritical to give humans government benefits that companies don't get?
This would incentivize future companies to operate a bit more conservatively. The pattern of corporate irresponsibility followed by taxpayer-funded bailouts is a moral hazard.