The buyers in the two cases I'm thinking about would have never been approved by any regulatory agency and those huge losses would have never happened. 

Two different clients, both military, both landlords, both with sufficiently high incomes (>$150K when filing jointly with spouse) that their passive losses from real estate investing are suspended.

We are not responsible for items damaged by the failure of the appliances or the supply of water/gas/power to those appliances, including but not limited to the loss of food.

Being in Los Angeles and the risks associated with it, making $600 more that year means I'm at a loss knowing I would have a month of vacancy plus the cost to prep it for rent.

You will lose the money that you pay on the tax lien, but you will get back all of your overage as well as the interest that was due to you thereby minimizing any loss.  

Can a tenant be sued SUCCESSFULLY for loss of income if they left behind damage that requires time and money to repair and prevents the apartment from being rented to new tenants?

Do you have loss of rent coverage on your policy?

Sometimes even a small loss to free up debt is worth it in the long run. 

So I could put the house back on the market after that, though I would take a decent size "loss".

He has close to $3,000 in unpaid water/sewer bills, a stolen furnace, and no insurance, a property he owned for three years and had exactly two tenants, one for two months, the other for six(but paid only three months) and now has a dilapidated property that he's going to sell at about a $30k loss.