You need right about 2000 calories a day to maintain 130 pounds if you typically have light activity (rather than vigorous exercise). A pound represents 3500 calories not eaten.
Fast for a week and that's 14,000 calories not eaten. Divide that by 3500 and your get, ah, just a sec... four pounds.
Four. Is that all? Worse still, it's likely to be lost muscle mass, not body fat, because that's what happens when you stop eating. Your body saves its fat stores in a last-ditch effort to keep you from starving to death, and gives up muscle tissue to meet your energy needs. It also induces lethargy, slows thinking, and increases need for sleep, all calorie savers.
The bad thing about losing muscle mass is that when it's doing nothing but existing, it burns calories. Losing it (and not fat) pretty much guarantees you cannot maintain a lower weight.