A real and common problem with old bottles of wine is a crumbling cork, which can happen no matter how well the wine has been stored and is, unfortunately, not one that is easy to predict or prevent. But the older the wine, the more common it is.
Sometimes it’s the top half of the cork that will disintegrate, leaving the bottom half firmly lodged in the bottle neck. Other times it’s the bottom bit that crumbles into the wine, and sometimes it’s the centre that turns to powder as the corkscrew pushes through, leaving the outer parts of the cork stubbornly stuck to the glass.
Some people use a two-pronged cork extractor, also known as a butler’s thief or an ah-so, which has two slim flat blades. These are gently inserted into the bottle neck on either side of the cork rather than through the cork, twisted and very gently pulled. See pictures below.
If there is no butler’s thief to hand, you can sometimes rescue a partially crumbled cork by inserting a long, narrow corkscrew into the cork at an angle, however, it may be easier at that point to very gently push the remaining part of the cork into the bottle using something like the back of a wooden spoon. This can cause a splash, so wear an apron.
To avoid bits of cork floating in your glass, pour the wine into a decanter or jug through a funnel with some kind of filter. It does expose the wine to air, but then that may well not be harmful. The cork itself is neutral and doesn’t taint the wine (unless it is one of the small proportion affected by cork taint or TCA) but the texture of cork particles in wine is not particularly pleasant.
There are nifty stainless-steel wine funnels that you can get with fine-mesh filters (see picture below). These can be fairly easily sourced via the internet. Alternatively, a clean coffee filter or muslin will work well if rested in a super-clean funnel.