Losing a coworker, particularly at a small company, is also quite traumatic. After losing a key member of a team, perhaps the survivors find they have other priorities in life than trying to file for lots of patents. This seems like a rather obvious confounding factor.

Exactly, seems pretty disingenuous to measure grieving people's productivity and compare based on whether they're grieving the death of a native or immigrant.

If they were from another country and I didn't even have any of my cofounder's family around, just a big gaping hole where they used to be... I'd probably quit and go find a job somewhere else so I could stop thinking about it.

Getting a patent application in would be the very last thing on my mind.

2) His death also meant the death of his creativity in his team. It also means that no one else could replicate it at that level? [That they couldn't find a replacement for him quick enough]

3) By how well it is received by an organization and real world customers.

Would you say that Steve Jobs brought life into an otherwise dull company called Apple? Not saying that immigrants are like him, but just throwing some light on your questions.

One patent can be more "innovative" than 10,000 patents. For example, 10,000 patents on horse carriage designs/parts compared to one patent for a Model T car.