There is nothing safe about unprotected sex. There are always chances using any type of withdrawal method/rhythm method, etc., for transmission of STDs and pregnancy.
There is no "safe" period for having unprotected sex. However most people have unprotected sex on their period as this is when the egg is released so there fore there is no egg there to get pregnant...
Most likely, but don't ever use the "withdrawal" method. Your risk of becoming pregnant is exponentially higher, so either tell your partner to wear a condom or get a prescription for birth control...