I'm not sure what you mean here. You can't write off a mortgage. You could write off interest, but not the value of the mortgage.
Real estate tends to appreciate in value, especially in cities. The company would have to get unlucky with their real estate to be able to write off a loss. Buildings don't usually depreciate.
They could allow their buildings to fall into a state of disrepair, hoping it would lower their value. But why would they? The can deduct the repairs. It's a legitimate expense.
As a business I can take out a mortgage and give you a rental for the exact same price. The income and “expenses” cancel out, so the profit of your business is zero. Since this rental is an income producing activity the IRS (and other tax bodies) allow you to depreciate (https://www.irs.gov/publications/p946) the value of additions on the land (I.e the building) on a straight line over a 28 year period. The basis of the depreciation is the value of the property, so you divide that over 28 years and can take that away from the income as well. Now I can transfer that cost to you in rent and the profit of my business is still zero. This is a benefit that is generally only available to corporations. Then there is prop 13 which is yet another mess.
I’m not an accountant, but I’ve studied enough of it in University to be dangerous.
It's fair that you don't pay tax when don't make a profit after taking depreciation into account.
Depreciation isn't a cheat code that lets you avoid tax on profit. If you depreciate the building more than its actual market value depreciation, you owe back what you deducted when you sell the building.
Real estate tends to appreciate in value, especially in cities. The company would have to get unlucky with their real estate to be able to write off a loss. Buildings don't usually depreciate.
They could allow their buildings to fall into a state of disrepair, hoping it would lower their value. But why would they? The can deduct the repairs. It's a legitimate expense.