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So you just pay the overstay fee .... And don't worry about being in the country illegal*
You are not "illegal" due to the fact that you overstayed a tourist card, because the Dominican government has a system in place that addresses this. Paying the departure fee upon leaving. If this system, which is their's, was not in place, than you may be considered illegal as in other countries. Do not confuse other countries' immigration laws with DR's. Every country is different. Again, this is their system.
Now, the term "illegal" would apply to EWI's. EWI's are the same the world over, in that you Enter Without Inspection. This applies when a border or immigration officer of that respective country did not inspect/register/or whatever their system accounts for regarding your documents (passport, etc) and you. If you arrive in the DR and obtain the 30 day tourist card, and overstay the 30 days, you are not considered "illegal", rather that you have just overstayed your tourist card and have to pay the fee upon departure. If you enter the DR under the cover of darkness, through the hills of the Haiti/DR border, in, in back of, under, or on top of a vehicle, on a yola or any other type of inflatable/floating device or even decide to parachute in, and are not inspected by a border or immigration officer.....then you are illegal. Also, if you enter the country through one of the checkpoints...border, airport, etc.....with falsified documents....then you are illegal as well. Simply overstaying 30 days is not the end of the world. Try it, you'll like it. Just remember to have cash pesos on you upon departure. No credit cards accepted.