That's 50% chance of going to zero and 50% chance of doubling, not business as usual. I don't see what's so unusual about it. For example, if you buy an option (a financial instrument, a call or a put) and it expires out of the money, it's worth goes to zero. That happens all the time and no one calls it UTTER RUIN. Of course you may not want to invest your entire worth into one...
Or if you want a stock example, imagine a small biotech company with a single drug going through FDA trials. If the drug fails, the company is basically worthless, if it passes, the company is rich. That's a double-or-nothing scenario and again, not particularly uncommon in real life.
By your hypothesis the stock has a 50% chance of utter ruin and a 50% chance of doubling every day. That is very unusual.
Let's suppose you start with $1000 to invest, and the only thing you can invest it in is stock ABC. You are only permitted to occupy two states:
* All assets in cash
* All assets in stock ABC
You incur a $2 transaction fee every time you buy or sell.
Kind of annoying limitations to operate under. But you have a powerful advantage as well. You have a perfect crystal ball that each day gives you the [probability density function](http://en.wikipedia.org/wiki/Probability_density_function) of ABC's closing price for the following day (but no further ahead in time).
What would be an optimal decision rule for when to buy and sell?