This is actually the your (the landlord's) mortgage, not someone else's. That is one part of the risk of an investment vehicle that allows more tax write downs than most other investments.
Just like other investments, the pain is much less dramatic if you aren't over levered. If you are, profits are good until they aren't. Higher risk comes with that higher reward.
However the cheap leverage and massive influx of foreign investment kinda fell off which made prices drop like a rock in 2008. I wouldn't be surprised to see it happen again in late 2020 and 2021 when a bunch of people see balloon payments from deferred mortgages.
Just to be clear for other readers. The only special tax write downs for real estate is depreciation, which isn't a write-down, it's a deferral. (OK, yes you can escape the deferred tax by dying)
Having a mortgage is irrelevant to the tax situation. Mortgage interest is not treated any different than interest on any other business or investment financing. Even the margin interest in our brokerage accounts is deductible.