If people are unsure as to what is 'right' for their situation, I tell them to consider the pet -- if the person is very emotionally upset, some pets become stressed upon seeing their human distraught. The euthanasia drug itself is an overdose of a barbiturate that stops the heart and breathing muscles. This is administered through an IV catheter or with a needle and syringe. Things to be aware of as death occurs: 1  the eyes don't close.