There should always be 2 kinds of "death" one is where your character has the shit knocked out of them but is able to get up and walk away after some time.
The permanent kind of death is rather obvious, you are dead.
The question then becomes how can this be weaved into a game well any game can have "playing possum" where most instances the AI disregards you if you are still enough then from there either friendly AI being able to teleport yourself out or setting up a event where a day passes and most things ignore you you could have rats annoy you now and then or even have thieves come upon you then depending on how you are healed up from it and the encounter there after drag yourself back to town badly hurt this could also be implemented by not spawning many if any "opposition" on your journey to sanctuary.
This could be simplified into something that would not be to annoying to causal players then up it to where you are basically crippled from a bad fight and you must rest and you must take a few game weeks to recover you having money will make the process faster but if you have none you can relie upon charitable organizations and the groups you have allied with to heal up, this of course is a RPG/living world type of deal that requires auto save to be used before a encounter starts up.
In a less RPG driven game just being still for a few minutes so you can pop up and hide could work but I think it disrupts modern design themes so much no one would bother with it.
Now lets get back to the meat of the OP as for making a game with permanent death it truly has to be an option, then you have death where you die that character is gone done over if you wish it to be so.
Then you have the next character able to get a hand full of items(1-5) and a portion of combined wealth to the next character, you receive it from family,ect but indirectly to the bloodline/story of the old character, plus you can visit where you died and find all the items within the region(at stores or in pack rat animal/monster locations )or on the body itself.
Combat would have to be tweaked so you have half or less damage to your locations,ect where enemies are rather easy to kill or at the least easier to kill than you, also a need different kind of health system needs to be used perhaps have a heath meter and a "threat needle" that jumps all over the place when damage is calculated, most damage cools off quickly and dose not harm you to the point it lowers your health if this kind of damage continues then it drains you, this means most damage that is accumulated is a warning that your health is at risk rather than a direct assault upon it.
If tuned and polished it could be used without making enemies too weak .... now that I think this is akin to a regeneration system think halo ONE (when you think halo think 1, 2 and 3 suck >>) with a larger shield, the shield is your sense of pain and of lite wounds that can be ignored. If you use items that are meant to distract when you get low on health you can bolt from a fight.
You health is everything if its low you need to find cover or die.