It's not a requirement for "everyone else to pick up the slack". That's just the businesses choice.
At the end they could choose to let the team be less productive. Business should already assume that they may lose an employee at anytime, or roadblocks may come up, so if they're assuming the teams are always going to be at 100%, that's probably not realistic.
The business could also: hire another manager, or promote someone whose been looking for an opportunity to learn to manage. If they do want to shift the load to other existing employees, ideally the business is structured so that other managers aren't at 100% capacity and can help fill-in temporarily. That's still a form of "picking up the slack", but if it's planned for, it's usually less an issue.