There is plenty of speculation about the humungous volume of data that the LHC produces and is thrown away. The data that are collected go into numbers that no brain can handle.

So the thinking at the peripheries is
1) that the unused data could reveal something.
2) there are second (etc) order interactions that are revealed only by the debris in the data.
3) you only see what you are looking for (hence the unused data).
4) and new pet theories that focus on specific data (as per 3).

Let's see what pops out in the next 50 years - but send me a message from the future, 'cause I don't think I am gonna make it that far.