I was a restaurant manager back in the mid 90's. That was exactly how we handled it. All I asked is that they notify me as soon as they knew they weren't able to make it in so I could go to the office, pull up the list of contact info, and start calling folks to see if they'd be willing to put in an extra shift. I would also negotiate with them for things like an extra day off, a free meal for them and their family, basically anything I could do (outside of extra pay, because I wasn't responsible for that part).

If nobody could cover it then I would fill in when I could at their position. Why? Because that shift is MY responsibility. If an employee can't work then it's on me to make sure MY shift ran as smooth as possible.

Any shift supervisor or manager who tells their employees to get their shifts covered needs to re-evaluate themselves. Shift supervisors and managers get paid more because of the additional responsibilities they have, and that includes staffing properly to the best of their ability.