Cutting back very mature shrubs

Having now spent 12 months at my house , I think that my mature garden is perhaps a bit too mature! I think some of the shrubs have been left to their own devices for too long. For example last summer what I thought was a tree because it looked like a tree was in fact a Rose of Sharon, it was a real disappointment when it did anything and didn't flower for as long as it should have. It has a lot of lichens growing on it and I can't tell what bit is dead and what is alive. I also have what I think is a type of hebe ( the same variety repeated several times over around my garden!) Most of it looks ok but some of it has become tall, straggly and with a very thick stem and looks horrible.
When shrubs have been left so long unchecked, will cutting them right back kill them?