You are looking at needing Family Base. Unless it has been changed, once the device reaches its limit, it will receive no more mobile data but CAN access the internet through WiFi.
TESHA122, you have a great question at hand. Please tell us more, how are you adding the data block to your lines? Are you using the Verizon Smart Family program? If so, you have the option to add a block that will stop all cellular data use for that line, once its data limit has been reached. Here is a link to all you need to know about our Smart Family program. https://www.verizonwireless.com/support/verizon-smart-family-faqs/
Follow us on TWITTER @VZWSupport
If my response answered your question please click the _Correct Answer_ button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!!