The question is whether that person who hasn't done martial arts in a long time has done anything to stay in shape over the years. If they have been sedentary for a long time, they will likely need to build up to a base level of fitness first. This is just to get the joints used to moving, build up some mobility, and add a bit of strength. If they are already fairly active, they might be able to jump in and adjust well enough.
One example of the latter that comes to mind is someone I met in my teens. He was in his 50s, and could play basketball pretty much all day long. That person would be able to jump into Kung Fu, or any other martial art, and learn the way most beginners learn.
However, since people like that are rare, it might be worth doing a bit of a physical assessment and giving some homework to help solve the problems. Most common issues with getting older (and I hate to admit I'm approaching that) are:
- Increased need for mobility (this is range of motion, not just flexibility)
- Need to build up cardiovascular system.
- A need for basic strength to overcome sarcopenia, which starts about age 30 and robs up to 15% (in sedentary people) of your muscle mass every decade after that.
If the person is lacking in only one area, have them work on improving that area. If they are lacking in all three, then start with what you feel is most important for your art and build up from there.
The basic strength can be obtained through body-weight exercise. Mobility can be done either through stretching, or other exercises designed to increase the range of motion. Most likely hip mobility and shoulder mobility will be the most affected. The cardiovascular system can be built up rather quickly by running intervals. If they are very detrained, start with walking/jogging intervals and work up to jogging/running intervals. Tabata training is very effective (20s activity, 10s rest, 8 cycles).