Does a roommate with their name on nothing(lease,utilies,written agreement)and paying nothing have the right to a 30 day grace period to find other residence.

It really depends on what the tenant laws are where you live.

If the roommate has in fact taken up residence in the property, even without having signed anything, or paid anything, there are places that will place their rights above those of the Landlord or responsible renter.

The laws are sometimes well intentioned, but often go way to far to protect the guilty and punish the innocent. Tenant laws are some that I feel fit this description very well.

If you want a good example, even though it is fiction, watch the movie Pacific Heights some time.

Good Luck!