My brother and I have talked about
what we will do when our mom dies. Suffice to say she's a hoarder, and the state of her house creeps us both out. The thought of having to clean out her place led to some research, and we found that there's an entire industry built up around 'Estate Cleanup Services'. My guess is your mom's mortgage company has two or three of those companies on speed-dial.
I love your idea of having the neighbors come over and grab what they want from your mom's house! What a practical way to honour her memory.