Furniture that needs refinishing often needs some regluing or wood repair. It’s almost always best to do all the regluing, parts repair and parts replacements before doing the stripping. This is so that any glue seepage or damage you might cause happens on top of the old finish. When it is then removed with the stripping, so are the glue seepage and the damage.
The exceptions are when the wood is covered with paint or a heavy glaze and you need to patch or replace a part or some veneer but can’t see what the wood is. You will have to strip the paint or finish, or at least some of it, to reveal the wood.