In the general case, it is not possible.
As you cook meat past about 165 F, all of the proteins will have denatured and contracted, squeezing out moisture. This is what makes well done meat tough and stringy or rubbery. This process cannot really be reversed, although you can try to mask it with a sauce.
In the specific case of certain cuts--the ones famous for braises or barbecue, the "low and slow" cooking techniques--there is some hope, but it is a thin one depending on what you have been doing.
These cuts, the most active working parts of the animal such as the shoulders (chuck for beef or butt for pork) have a great deal of intramuscular fat, as well as connective tissue made of a protein called collagen.
Over time, when cooked slowly at temperatures of about 180 F, the collagen in the meat will turn into gelatin, which has a silky, smooth mouth feel, and the fat will lubricate the meat. They still have their proteins irreversibly dentures and tightened, but the gelatin and fat provide a new kind of moisture and unctuousness that is highly prized.
The cooking techniques for this (braising, barbecuing, slow roasting) are rarely employed for chops or steaks that you would do in the frying pan. They also simply don't have the collagen or the fat to make it possible. That is why they are better off with the higher temperature, faster cooking methods, but should not be overcooked, as you have discovered to your dismay.
Your best option is not to try to recover from this situation, which is very difficult to do, but rather to learn to prevent it:
- Get a good instant read thermometer to check the internal temperature of your steaks or chops
- Learn what the safe temperature is for that type of meat. For example, poultry and pork should both be cooked to at least 155 F (and for poultry, many people have learned to like even more done meat)
- The FDA recommends 165 F for ground meat (which is quite well done)
- Measure the temperature of your meat and learn to recognize when it is done
- Assess what level of risk you are willing to accept
Over time, you will learn to recognize when cuts are done to your liking by how they feel when you poke them with your finger (which is a pretty good indication of how done they are, based on how resilient they are), but the thermometer will be your guide until you build that experience.
Still, this will require that you adjust your expectations of what completely cooked meat looks like. Pork may still be a touch rosy, for example.