Are you fasting or can you just not afford to eat? If it’s the latter, please have a look at r/assistance - lots of us help others with temporary support to get people over a blip in their circumstances e.g. through an Amazon food wishlist. It’s one thing to fast, but another to starve, hope you are ok
You can’t harm metabolism to any sort of degree that actually matters. It just simply isn’t a thing. 600 calories a day however is WAY to little calories. Your body will break down muscle for energy at levels this low even if you are working out and getting enough protein (which you aren’t given your current calorie intake) You need to be eating at least 1200 PER DAY if a women and 1400-1500 PER DAY if male. You will still be losing good weight even at these levels though. It would be helpful to add your Gender, Height, and Current Weight to this post for more context.
Your metabolism will actually get better, problem is that if you are not getting enough protein in a single meal your body is not rebuilding itself, eat as much ground beef as possible to keep proper protein intake.Still lack of calories will eventually kill you no matter what, eat butter, is cheap and provides tons of calories. Also eggs, 20 per day will be enough to keep you alive and healthy.