If we find, for example, an ant dying because someone has stepped on it, what should we do? If we do nothing, it will continue to suffer. If we kill it right then, it will not suffer anymore. What do I do with an ant that is suffering because someone has stepped on it?
Buddhists do not advocate euthanasia. Ending suffering in this lifetime by putting an end to that suffering life is not the answer as the being has to reap the fruit of the kamma in the next life. The suffering is merely postponed to a future birth, as the suffering must continue.
Beings are born and die in different life cycles and periods until the final liberation, Nibbana, is achieved. If we see any being in suffering, we try our best to relieve that suffering. If we neglect to do that, it does not create any bad kamma because we are not responsible for that suffering being inflicted. We can only try to alleviate that suffering. If we cannot, we must move on.
Similarly, in a hospice we encounter many terminally ill individuals. You see so much suffering around caused by the devastating effects of cancer, paralysis, AIDS, etc that you could easily begin to feel remorseful, helpless and drowned by the magnitude of the suffering. But you must remain focused to do what you can do within your means or network and not succumb to helplessness if you cannot help everybody. It is important to remain positive within in order to help. Succumbing to a sense of helplessness does neither you nor others any good.