Rear stabilizer? If you mean the thin, kinda wiry bar that snakes between the two weels, that's the rear sway bar

I wouldn't worry at all. Even if, say, the bar snaps, you wont suddenly lose control and crash. You'd just have some odd suspension noise in the back and your car's handling would get sloppy.

If you want to replace it, though, Id look at the Comptech rear tie/sway bar combo. Top notch piece of equipment.