It's hard, but necessary. My cofounder and I just hammered out our Operating Agreement, which contains special language for exactly this scenario. Amid such tragedy, it's best to have the legal framework 'on rails' so that you don't really have to think about it. Anybody dealing with the death of a friend and business partner has enough on their plate already.

Here's our solution, in case other people are interested:

In event of the death of a member (we're an LLC), that member's economic interests revert to their estate, but the inheritors lose all power to vote or make decisions.

Within 180 days, the surviving member can elect to buy out the deceased member's interest at a reasonable valuation. There's some legalese in determining "reasonable valuation", but the upshot is that the surviving members may take complete control of the company so long as the inheritors of the deceased are properly compensated.

If a buyout doesn't occur, then the inheritors of the estate become silent partners unless there's a mutual agreement to instate them as a full partner.

Despite what some people say, vesting is not always the answer. A lot of vesting mechanisms leave the door open for somebody to get screwed out of their rightful share. Personally, I'd rather see someone undeserving get rewarded, rather than see a deserving person get shafted.

One more thing: To Rex (the OP), my sincerest condolences. Losing a business partner is hard, losing a close friend is orders of magnitude harder. I think I can speak for the whole HN community in saying that you have our sympathy and understanding.