This is a very very hard problem. The fact is that in a startup you own 50% because you are there working. Once one founder is no longer present it's very hard to claim the 50% is still valid.
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.
I just wanted to add a suggestion over the reasonable evaluation and the option to buy. In our startup, the company has taken life insurance on both founders and half of the insurance amount almost match a valuation we as founder agree on at the start of each year. This is mostly for the first year(s) where the company is not getting that much revenues.
So what happens if one of us dies is that their family will get half of the life insurance for their equity. The other half is to help the company cope with the fact one of us is gone. This may sound expensive, but in fact for guys in their thirties and in good shape it is quite cheap.
In my first company we arranged vesting over 4 years, 1/4 each year. Some people might prefer 3. Many investors will also insist on this as well.
True. But as cmos responded, this is why you vest equity. Ultimately, as macabre as it is, death is just an instance of the general case of a founder no longer contributing to the business.