I assume it will be similar to when a person is out sick or on vacation. Another person on the team likely could take over the work for a day, but realistically it just sits until they're is back.
Not really, realistically speaking it's now possible to use an agent to read code and make sensible summaries of a codebase faster than ever before, and it's exactly the thing you'd use to onboard yourself or someone else on the team.
So work stops until Claude is back? What if Claude comes back and costs 10x the amount? The answer is obviously that you'll "bend over" and pay, because the AI vendor who convinced you that Claude is so great owns you, your codebase, and by extension your company now.