I'm doubtful Eiki would pick up a critter (and she's not alive to die in the first place), but she might try and help in some way. Maybe curing people, though no fighting.

The most likely action she would take is investigating the source, she has a very accurate method of discovering answers. However she would never bring any sort of group with her or go for a smack down since she is very adamant about keeping her neutrality.