A tenant who wants to stay in a property indefinitely at the current rent could theoretically schedule an inspection and freeze their rent and lease.

The tax will be paid.However, Eamonn also mentioned the way for you to avoid paying that tax indefinitely including recapture of the 4 years of depreciation. 

If you use the personal car, make sure to keep detail record so that CPA can prorate the expenses between personal and business.This can include- oil changes, Maintenance, gas, repairs, parking, tolls, and depreciation.

In my jurisdiction I would leave a unit empty indefinitely before renting to anyone on any form of government assistance.

I've also stayed in AirBnBs in gated communities; they just provide the door code and the guest lets themselves in. Definitely

Surely they can’t just leave their stuff indefinitely, without returning, without living in the place and without paying rent and my mom just has to deal with it.

I'm pretty concerned about market prices right now, but I also don't want to wait indefinitely for a market correction.

If you want to get something at $85 cents on the dollar you'll need to keep doing what you are doing but expect to be waiting a long time if not indefinitely. 

3. 1031 exchange - When you sell the property the portion you used as an investment can be used in a 1031 exchange - A process through which capital gains tax may be deferred while selling and buying an investment property.Advantageous financing, Tax free income from the sale, and indefinitely deferring the tax on the rest of the sale.

My two cents...if I am not selling a property, I don't care if it's worth a million dollars or a penny, property values are inconsequential to me for a place that I plan to keep indefinitely.