Sure it can, if the situation has gotten so bad that you need drastic measures, it makes sense. It's not ideal, but that's a totally different thing that "making sense". People have to make hard decisions with temporarily uncomfortable and problematic consequences all the time at the executive level. Getting rid of a big chunk of the workforce is hardly uncommon in terms of drastic measures, no matter how it's done.

And to many people, this is going to make Basecamp appear more attractive not less. They won't have a hard time filling seats.