I'm sure there are some who will willingly hop on a plane across the world without a second though and feel perfectly comfortable staying with a complete stranger for a week. On the other hand, there are probably women who require a copy of your passport, birth certificate, and a full blood test before they'll even consider meeting you lol. It really just depends.
For me personally, I'm somewhere in the middle. I already have a fairly thorough screening process, so if I do agree to meet you, I already feel comfortable as far as safety is concerned. My biggest concern with fly me to you dates is whether or not we'll get along for the length of time you'd like for us to spend together. For domestic travel dates from 6-24 hours, I don't mind flying out to meet you and seeing how it goes. I always book my own flight and room ahead of time, so worst case scenario I can hide out in there until it's time for me to go home. But there are very few reasonable people with whom I can't manage to make it through 24 hours. Longer dates and anything requiring international travel, however, I will only accept from clients that I've already met. It just isn't fair to either of us to waste that kind of time and money on a trip that might end up being an awkward, miserable mess if it turns out that we don't get along as well as we would have hoped.
Other safety precautions include the obvious: Having people at home knowing the exact details of my travel plans, being prepared to book my own lodging should things become uncomfortable or unsafe, having an internationally capable phone, etc...
I'm sure you'll get a different answer for every provider you ask. It's an immensely personal choice and everything from the client to the destination to the length of time may affect the answers. Hope that helps give you an idea of one way to handle it, at least!