From the Dzogchen POV, I think one could say that birth, life, and death are likened to seemingly separate permutations within a single dream. When one recognizes one's true nature and the nature of all things, one recognizes that there is no actual birth/arising, life/abiding, or death/dissolution to any phenomenon. If this is realized in a very direct, actual way, it's undoubtedly liberating. But for those of us whose understanding is more intellectual, thinking about it that way may or may not help with the pain of loss. I suppose it could for some, if their intuitive provisional understanding of this were particularly strong... But for most, relative level practices such that might assist their departed loved one find a favorable rebirth might be of more immediate consolation than Dzogchen perse until and unless one really has discovered rigpa.
One thing that is a major consolation and help for me when losing people I care about is the neydren ritual that takes place once a year here at Tashi Choling. Neydren basically means "hooking" the consciousness of the deceased person and directing it to a buddha's pure realm, and this can be done regardless of how recently the person died or any other factors I can think of (though it's only ever done once per individual). If possible, one uses a photo or hair or ashes, or a piece of some unwashed item of clothing belonging to the deceased as a support. Some great master such as HH Getse Rinpoche, Yangthang Tulku Rinpoche, Lingtrul Rinpoche or another acts as Vajramaster and is the one performing this in actuality, though the whole sangha of practitioners practices along. The neydren is held every year around July during Tashi Choling's annual Dudjom Tersar Vajrasattva retreat and items to be used as a support can be mailed in if one can't attend. Also, the ashes of all these supports (which are burned during the ritual) are used in the end to make Amitabha tsa tsa's which are then placed in Tashi Choling's Amitabha shrine. Here's a link to last year's neydren flyer: http://www.tashicholing.org/pdfs/neydre ... 202010.pdf
It seems to me I'd heard in the past that some other Nyingma centers also do neydren annually, so if anyone's interested, it's something that you can look into. This may be practiced outside Nyingma but I don't know. I do know that in the past when a loved one had died, the ability to include him or her in this ritual has been a great consolation to me.