If you embezzle, especially if you steal public funds for your own private use, then you peculate that money. To peculate is, of course, illegal — if you're caught, you can serve jail time.
Peculate comes from the Latin word peculium, meaning private property, which itself has the root pecu, or cattle, so the literal meaning of peculium is "property in cattle." Cattle were considered very valuable property in ancient times, and stealing them was a grave act. Other words that have pecu at their roots include "peculiar" and "pecuniary." Despite the extremely similar spelling, the word "speculate" has totally different roots that have nothing to do with either cattle or embezzlement.