This question is being asked for my friend who is an inmate. "I have gone from doing 1000 push ups every day (what else is there to do here?) with Sat/Sun rest days. To doing 1000 on Monday and Thursday with 2 day rests in between. Feel that I am losing any gains from original plan. Which is the better routine?"
Doing anything at that severe high volume will eventually not become as useful as it originally was. With any exercise, if you keep repeating it your body will adapt to become good at it and you will plateau.
If he has a lot of time and wants to improve his fitness, suggest some of the exercises listed here: https://www.reddit.com/r/bodyweightfitness/wiki/training_guide
There is progression there and a opportunity to do some very impressive exercises that he will find much more beneficial than 1000x of any single exercise.
Building on JJosaur's answer, there's also the issue of muscular imbalances.
Chest muscles pull your shoulders forward. Back muscles pull your shoulders back. If one set of muscles is completely over-developed compared to the other, your posture, and in turn your back, will take a severe hit in the long run.
This is usually never a problem for the case of back muscles overpowering the chest muscles. But the other way around is quite frequent, and if you pay attention, you can literally spot people every day that suffer from this, unknowingly or not. They'll be hunched forward over a hollow/concave chest.
Doing thousands of pushups every week can very easily lead to this, but thankfully, there are bodyweight exercises for your back as well, namely pullups. I would think that a person who can perform a thousand pushups in a day will be able to do at least some pullup variation.