Sounds a bit strange, doesn't it?
First, it's easy to talk about what I don't mean. This is not a suicide cult site, or anything associated with destructive behavior. "Loving Dying" does not mean "enjoying killing."
Loving dying as a term that works for me on a number of different levels. First, hospice care is my life's work as a nurse. I got into nursing because of an experience I had attending a friend's death. My career track led me to end-of-life care. Caring for the dying in my case is the classic Right Livelihood, that is, something I get paid to do that I would gladly do for free. In that sense, I "love" working with the dying. I find the work fascinating, meaningful and rewarding.
Second, I think it is best when a person dies surrounded by an atmosphere of tranquility, acceptance and tolerance. That is, what can be called a "loving atmosphere" is best around someone encountering the end of their life. In this sense "loving dying" means fostering an atmosphere not unlike that which greets almost all of us when we are born. Even those with unique and emergent birthing circumstances, in the back of a New York City taxi, for example, have someone there who is committed to being a compassionate and skillful presence. I think we all deserve the same when we die and I've made it my personal mission in life to do all I can to manifest such around me. I want everyone to experience loving dying.
Third, it's an attention-grabbing and easy-to-remember word-blurb. Two gerunds, they sound alike, but they jar the senses when crammed together.