My sister lives in Ohio in an older house where pipes freeze. Recently a pipe burst. She is being told that there are new pipes available that will not burst when frozen. Can that be true?

I know of no piping that will not burst, Pex piping is suppose to with stand freezing better than other types of piping but even it will bust under certain conditions.

NO.

Watch this video demonstration and it will give you an idea of what types of pipe will not freeze and fracture:
What happens to water if it's not allowed to expand when frozen? – The Blogs at HowStuffWorks (http://blogs.howstuffworks.com/2010/04/27/what-happens-to-water-if-its-not-allowed-to-expand-when-frozen/)
Hint: None

Look for manufacturer's who make a claim that their type of pipe won't fracture if water freezes: Once again, none that I can find.

Has anyone ever encountered a situation during cold weather when their water ceased to flow, they assumed it was completely frozen, but with the passage of time and/or application of artificial heat and/or rising atmospheric temperatures, it started flowing fine again, and there was no leak to deal with? Absolutely. It happened to me once where all copper was being used. It happened to my mother's old galvanized service, and many others I am sure.
I believe that when water stops flowing, and we assume it is totally frozen but luck out and it finally starts again (for any of the reasons mentioned earlier) with no leaks, the water never froze completely. Like the water in an ice cube tray when you were in a hurry to make some more ice for the party coming up or going on, and you pull out the tray and at first glance you say- ah, ice cubes finally, then look and see the water bubble in the middle of the cube. That's my theory and I'm sticking to it.

Water expands 10% when it becomes ice (according to the video). For a 1 inch pipe, that means that the inside diameter has to go from 1 inch to 1.1 inch, or roughly, 3/32nd of an inch increase in diameter. If a pipe of a type other than steel or copper (cpcv, pex, etc) was somehow encased such that its outside walls were totally immovable, maybe (big maybe) the walls could be squeezed (COMPRESSION) 3/64ths of an inch (1/2 of 3/32) because it was a pliable material (maybe again), but in the real world that is not the case, the walls of the pipe are subjected to TENSION.

I wish they made pipes that didn't burst. It would make our work a lot easier. Unfortunately there is nothing on the market that fit that description. When I can suggest would be to use heat wraps. Good luck, Tom

This site won't let me edit or add to my post flow of a new one. Here are some and inches of heat wraps. Hope this helps, Tom