How to deal with split objects due to tiling

What is the correct way of dealing with target bounding boxes being split due to the use of tiling? Would you still keep a bounding box annotation on a tile even if a very small portion of the original object is showing? Or is there some threshold you establish that would work as another hyperparameter were you only keep the annotation if X% or more of the original bounding box is showing?
I suppose there are different approaches I’m just curious about what some pitfalls might be. With the threshold approach I’m just afraid that it can feel very arbitrary and can lead to conflicting annotations and bad learning.

Thanks.