I entered Dubai on a 30 day visit visa but did not leave within its validity. I have now secured employment. My employer has obtained a work visa and residency visa for me. Does the law allow me to continue to remain in Dubai and to work or must I first leave the county and then renter on my work visa? Am I breaking any laws if I continue to live and work without leaving the country?
If the new visa is stamped/attached to a page in your existing passport, then most likely you are good to stay in the country. If it is a 'visa' on arrival to activate then you must re-enter the country to start the visa.
If your new visa shows you needing to arrive after a certain date, or not valid before a prescribed date then you will need to re-enter. Your employers visa agent should be able to manage the cross over time.
On a side note, if you leave the country to start the new visa you should stay outside the country for 24 hours (not a 2 hour turn around flight) in order for the immigration rules to validate the new visa as 'new'.