If I claimed myself independent on 2020 taxes and my parents dont claim me on their taxes, but I live with them. What will happen?

Regardless of the actual facts, as long as your and your parents' tax returns don't disagree, the IRS has no particular way to find out you were lying.

From a legal/technical point of view, if you can be claimed as a dependent, you must answer "yes, I can be claimed as a dependent" even if you don't want to be claimed.  For 2020, answering "no" when you should answer "yes" will result in you getting a recovery rebate in your own name that could be considered tax fraud.  However, even if you live with your parents, you don't qualify to be claimed as a dependent by them unless you 

a. are a full time student under age 24, or

b. are any age, but your parents paid more than half your financial support AND you earned less than $4300 taxable income.