If it's the only currency in Ecuador, the price of a house in Ecuador in bitcoins doesn't have to match the fluctuations of BTC<->USD. If Ecuador also tightly controls exchange with foreign currencies (which they likely already control, just not tightly?), then they can make the value of bitcoins within Ecuador as stable as any other currency.

As for how they would acquire bitcoins in the first place, all they have to do is mine enough for most citizens to access them and then distribute them. Or fork off a new blockchain with a different cryptocurrency that can only be mined by the central government (say, because it requires private keys to mine that only the government controls).