If someone has a trademark and they let it run out can I buy it and use it?

The mere fact that a trademark registration has not been renewed and has expired does not necessarily mean that you can use it.  On the other hand, if you can establish that use of the mark has been abandoned, as opposed to use of the mark merely having been temporarily suspended, then you could use  the trademark without paying the former owner of the trademark.  Failure to use a trademark fo three years raises a presumption that the trademakr has been abandoned. You need to investigate the situation in greater depth to know whether or not the trademark is available for you to use.