I wouldn’t go below about 0.5 times your lean body mass in grams of protein a day.  For example, if you weight 150 pounds and have 30% bodyfat, the lean mass is 105 pounds (150*0.7).  Then your protein minimum would be 52.5 grams (105*0.5).  So don’t go below about 50g of protein a day for any significant length of time. 🙂