Sorry for the delay, I'm having some issues after Windows 10's last update, as are some other people I've been assisting.
It depends on the shrub and the circumstances. I just had a lilac heave over and break in some minor winds that Fay brought. I let it get too tall, too leggy, and overfed. This was my fault. I cut it back hard, but it's actually a bit late. It's not going to bloom well next year, if at all. But the shrub itself will be fine and, fed appropriately, will also regrow a lot of greenery by August.
As a very, very general set of rules for which there are plenty of exceptions, so always check for the shrub individually:
Shrubs that bloom yearly on new or old wood: Cut right after blooming. There's always a window, often a wide one, but this is rarely an error. As a very general rule, you can cut up to six weeks post-bloom and still be just fine, unless that starts to move into frost and freeze.
Repeat bloomers: These can sometimes be cut back after their first major flush of bloom so that you get to enjoy that, or wait until the very beginning of the season (as with caning roses). With these, check the individual plant for the best practices as they tend to vary a lot. And also realize that the shrub tends to let you get away with a lot, too. I don't follow the rules very well on my roses and...they do fantastically well, actually.
Most Woody Shrubs: Always check, but again, it's usually not a major mistake to cut until eight to six weeks before frost. Many dislike having all the greenery on a branch removed, so don't do that.
Some don't care. Your boxwood and my lilacs don't care and will happily resprout from any growth point. Most evergreen shrubs, cut back to brown, will simply stay brown at that point. Some shrubs will start to look like trees if you cut them back to the "trunk," which can be an interesting form. Most of our shrubs actually do flower, if unobviously, so again, you're probably giving that up.