Every UAE visit visa or Dubai tourist visa has a stipulated time in which you can stay in the country legally. After this time, if the visitor is supposed to exit the country and if they don't, it is considered a visa overstay, which is illegal. The UAE government has clarified that tourists should not overstay their visa to Dubai under any circumstances.
Overstaying a tourist visa for Dubai can result in severe consequences that could even lead to travel agencies filing absconding and getting blacklisted. Once blacklisted, the visitor could never enter the UAE or any other GCC country.
The visitor would also be subject to penalties which include fines, imprisonment, and deportation. So, it is important for a visitor to apply for Extended Dubai Visa or UAE Online Tourist Visa before his current visa expires.