Not really a way to delete an action without it being the current animation, unless you could locate that action in the outliner. Dunno about that, never tried that before, but it just occurred to me.
Sound like, from your first post, like the .blend file is corrupted. It’s rare for that to happen, but it does happen. A good way to over come a corrupted file and/or delete the action without opening it is simple… Start a new blender session and delete everything. From the file menu, choose append, then open your bad file. You’ll now have a few folders, go into the objects folder and choose everything. This will select all the objects in your file, your armature object, mesh object, camera & lights objects, etc… Now go up one level in the file browser (think it’s an up arrow) and choose the actions folder and select all the actions but the bad one, and hit append. This copies all the selected data from the file to the current session, save with a new file name and test it out.
Thinking about this a bit further, the bad action might have scale key frames inserted in it, remove them and reset the scale should clear it up. It can happen being new to blender, a few wrong keystrokes and mouse clicks and boom, something bad happens. Speaking of being new, since your also new around here, lemme just say: posting the .blend file is most helpful. It allows someone to look at everything, and not just guess based upon your description. At first, I was thinking corrupted file, then as I thought about it more while typing, I’m thinking more and more it might be an erroneous key frame causing this.
Welcome to the forum!