Yes, it is true that the NYS DMV can deny issuing you registration on the vehicle thus you cannot register and use the vehicle since the current registration has been suspended as a penalty for having a lapse in auto insurance coverage.
The New York State Department of Motor Vehicles (DMV) states that they will not issue a new registration if the DMV determines that the purpose of the new registration is to avoid the suspension. The NYS DMV will not issue a registration if the applicant for the new registration:
- has the same last name as the registrant whose registration is suspended, or
- resides at the same address as the registrant whose registration is suspended.
The DMV will not issue a registration to any person unless that person makes a sworn statement on form FS-2. The statement certifies that the purpose of the application in not to avoid the results from the current suspension. The local DMV Office determines if the application will be accepted or rejected.
[Let CarInsurance.com help you find affordable auto insurance now.] As you and your mother are now aware, in New York State anytime that your vehicle is registered but not insured in NYS it can cause a lapse in your insurance coverage and suspension of your registration. In the state of New York the DMV should notify you once they are aware of a lapse in your auto insurance by a letter. This letter will give you instructions on how you need to prove you have insurance or sold the vehicle. If you cannot prove you this, you will need to surrender your vehicle's license plates to the NYS DMV, if appears your mother has already done this. If she has not turned in her plates then it is recommended that she gets a receipt when she does go into the DMV.
In NY a car owner may not be required to surrender your plates for a lapse of 90 days or shorter if they pay a civil penalty fine. If the lapse exceeds 90 days the car owner's driver license will be suspended. As in your mother's case, if you have a lapse in your insurance coverage in New York State and do not surrender your vehicle plates immediately, your registration is suspended for the same number of days that you did not have insurance coverage, but did hold the vehicle plates. If the time is more than 90 days, your driver license is also suspended for the same number of days as the registration. To reinstate your driver license, you must pay a termination fee of $25 when the suspension ends.
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If you do not have insurance coverage and you do not surrender your vehicle plates to the New York DMV, your registration and driver license are suspended indefinitely, it appears that your mother did turn in her plates though so this will not apply in her case. The NYS DMV itself should be able to explain to you more about why they refused to register the car in your name in this situation if you need more information on this topic.
New York has harsh penalties for those that have a lapse in auto insurance coverage. That is why it is important to keep coverage on a vehicle at all times, even if out of the country one must make sure their policy is up to date or find a way to turn in the registration and vehicle license plates so that penalties do not get assessed. | 
