Selling the House IS No Solution
What you can buy with the proceeds of a sale is so much less than what you are leaving.
My strongest reaction facing infinite 11% or higher rent increases every year was to sell the house and buy something else, something on land that I own. I looked at a map, did some Googling, called a few realtors and started looking at houses. Besides stick-built houses there are mobile homes for sale sitting on their own land. In fact less than 50 miles from where I live there are several mobile home parks where the residents own the land.
Seven Hills Members Club in Hemet is one such. A Youtube walk through of one of their houses
https://www.youtube.com/watch?v=6ugfcC1vn1Y from 2011, no price given.
So I checked recent ads (April 2014). These houses sell for $140,000 to $250,000. Too rich for me, alas.
However, in the area there were mobile homes on land I could afford. I will not name the park, but the house I walked through had security bars on all the windows, the steel security front door had been jimmied and hung ajar. I didn't want to live there.
Some of the other "owner owned" mobile homes in resident-ownership parks had been bought up by a few individuals and were being rented out. Attempts to discourage or stop the practice had resulted in lawsuits with legal fees driving up the association dues to the middle 3 figures. The large numbers of tenant occupied mobile homes had resulted in increased crime in the area, a decline in property maintenance, and in general a lowering of the desirability of living in such a place.
Moving to the country
Another option was moving away from a city into rural areas where putting a mobile home on land is commonplace.
I viewed this house in Lake Isabella, 4 hours away from where I live now.