Is it safe for a woman to have sex during her period?

Yes, and it's not uncommon.

Is it safe physcially, yes, it will not hurt either party.

Is it safe as in not becoming pregnant, no, it is possible to become pregnant if you have sex during the period.

I just reread this - I assumed it meant physically safe BUT I also should have mentioned that STDs (both serious and "casual") can be transmitted during unprotected sex, period or no period.