I mean, that seems obvious, there can't really be inflation if the money supply doesn't increase, can there?
If the money supply stays fixed, then some people will save/hoard money. Some people will also be more able than others to acquiring money (possibly because they already owned assets/rental property), maybe they were born rich. The amount of money that is circulating will automatically decrease. That tends to produce deflation.
The problem is that if you have deflation in your economy, it also increases the incentive for people to save/hoard money even more. Why would you spend your money today when it will be worth more later? You have a feedback loop where the amount of money circulating just keeps decreasing, and so prices automatically have to go down.