It all depends on what you need to do with these files right now...
If you need to use them without modifying them, you can use the option to open 2016 files in SWOLIDWORKS 2015 SP5 (and only SP5). These files will be usable for assemblies and drawings but not editable. The advantage is that when you go back to 2016, they will have kept their design tree. This partial backward compatibility was introduced when SOLIDWORKS 2014 was released, but was temporarily interrupted when SOLIDWORKS 2015 was released due to a large file format change. This feature is back with the release of SOLIDWORKS 2016 and the SP5 of the 2015 (EDIT: I just checked on an Early Visibility version of the 2015 SP5: the feature is available).
If you need to modify them, the only solution is to ask for a conversion to Parasolid (be careful to ask for a version of parasolid compatible with SOLIDWORKS 2015). The major disadvantage is that you will partially lose the design history and that you will not find it in 2016 since you will have modified them in the meantime.
Can't restore a previous version of your file or the entire folder that was before it was opened on SW 2016? ( Right click and * restore previous version* )