Yes, during cosmic inflation for example: two test objects initially close can end up many light-years apart. If we make these test objects null (i.e., lightlike) then we can always contrive an inflation that stretches them apart in such a way that they still meet again.
Some exotic spacetimes involving pp-wave sandwiches can focus initially non-converging and spatially distant light pencils onto each other at a caustic shortly after the passing of the stack of plane-parallel gravitational waves. One can hide some such processes in the early cosmos.
Some exotic spacetimes involving pp-wave sandwiches can focus initially non-converging and spatially distant light pencils onto each other at a caustic shortly after the passing of the stack of plane-parallel gravitational waves. One can hide some such processes in the early cosmos.