Yes, a trained 60 year-old can outfight an untrained 20 year-old, provided they maintain a healthy body. The average 60 year-old has already lost joint flexibility and mobility, which causes the body to start to become decrepit. A decrepit 60 year-old will always lose, even with training.
You should have no illusions that this is easy. You are probably not willing to put in the work this requires.
You must assume that others will be faster and stronger. Everyone's body will decline with age; you will not have the same strength or speed potential as your younger self. Honestly, I think everyone should train with this mentality, but I find this is frequently not the case.
Some martial arts encourage reliance upon strength and speed. Weight classes, for example, explicitly put you near strength parity. If you cannot get your techniques to work on people who are bigger and stronger when you are not old, you will not be able to get them to work on people who are bigger and stronger when you are old.
If the opponent is faster and stronger (and younger), how do you defeat them? You must move and fight efficiently.
- Use techniques that use the power of your whole body
- Apply force in ways the opponent cannot resist. Contrast force-on-force arm wrestling with foot sweeps, where the opponent's weight is suddenly unsupported by their legs.
- Apply force at optimal angles so less force is required.
- Find ways to move less distance so that even though your opponent moves faster, you arrive sooner. If you can strike at short distances with significant power, you have an enormous advantage over an opponent who needs space to windup, even if that opponent is stronger and faster.
For older martial artists:
- Train with someone older, who has been forced to understand the limitations of age
- Improve posture. This is about efficiency; poor posture has trained the body to work inefficiently throughout life, and you want to feel how sitting, standing, or moving efficiently feels.
- Improve joint flexibility.
- Learn to use your whole body. Some yogis can articulate each vertebrae in their back. This kind of control may be excessive, but it illustrates how a trained person has more control of their body than the untrained.
- Don't get hurt. I have had people tell me, "people can get really good at this throw, but they will probably damage their shoulder doing it". Find something else.