How to safely handle a phone with a (possibly) blown battery?

I took my phone out of it's case today and saw that it was bent in a way that resembles a blown battery. It is possible that I've been walking around with it for weeks without noticing, sincce it still worked fine, until today when it wouldn't charge anymore.

Thus far, I might've been lucky, but now I want to know how I can store it safely, or how to dispose of it. (I am thinking about looking for someone someone who can repair it or use it for spare parts and letting them have it, but obviously I obviously don't want it to explode till then. And also not afterwards.)

I managed to do a factory reset without it blowing up, but now it's turned off.