There is no monster
The whole scenario is just lizzys way of coping with the death of her mother. Her mom was an addict and died of alcohol poisoning (the monster). Her mom refused to get help and kept telling her she was fine (monsters aren't real). I think Jesse was probably someone who tried to help her with her addiction but couldn't and the paramedics may have been an incident where they tried to save her but were also killed by the "monster" (i.e.they were too late). In the end the mom finally admits she has a problem by telling lizzy "she was wrong" but it's too late the monster (alcohol) already has her trapped.
Now in the end lizzy states her mother was wrong about monsters and they are out there waiting. This was the writers/directors saying that addiction is real and everyone is susceptible to them. She then states she's "not afraid" meaning she's not afraid of following in her mother's footsteps and becoming an addict.