Traveled to Italy May, 2017. Before leaving signed up for $40 monthly plan so I could be ready to use phone on arrival. Constantly checked data usage on website to make sure I did not go over 100mb. On June 1st in the evening I checked on amount of data and had approximately 60 mb left, woke up June 2nd to notice of $50 charge for data overage. Just found out that when using data abroad, verizon does not know data usage until European data carrier notifies them. Hard to check when information is not available. My suggestion, if you need phone on arrival sign up for the $10/day plan that charges you only on days used. Then get to a local phone store to purchase a sim card. My husband was able to buy a card with 5kb data, talk and texting for $32.00. 3 of us used his phone as a hotspot and never had a data problem.
This same issue happened to me last year in Ireland. Last year figured it was my mistake for not keeping a better eye on data usage. Didn't realize it was just a great way for verizon to make more money off of us.