There has been some fuss of late from folks who get a huge mobile phone bill by not noticing and reporting when a phone gets stolen and missused. This can be prevented ..
When I bought a phone for use by a family member the best deal was pay by monthly bill with a generous call&txt allowance. To stop huge bills through misuse and in case phone was stolen and not noticed, I insisted that there is a max credit limit on the bill of £60. If this credit limit is ever reached outgoing calls are blocked.
This is the answer to prevent a huge unexpected bills from a loosely controlled or lost phone. The phone provider was 3 in the UK. If your provider will not impose an agreed credit limit to cap your liabaility, move to a provider that will. You can take you number with you so the hastle factor of moving is quite low.