You'll probably never see it happen. The Ancients used to do it all the time, but Dragons nowadays are softies. If you see one do it, though, pray it don't see you.
When certain creatures die, their Souls tend to linger about their body for a brief time. This can last just a few minutes to several hours. A particular phenomena that was first observed in the Ancient Dragons was that of Soul Fusion, or Soul Absorption.
The Dragon's Paradox
Two gargantuan creatures squabble for days, both on the edge of death, and when one finally succumbs, the other is perfectly fine; stronger, even.
Only ever occuring after duels to the death, Soul Fusion is now thought to have been very common among the Ancients, but it was seldom observed or studied; the fear of one's village/city being destroyed took priority for several eons.
Their observations began when they would notice one of the Ancients in battle grow immensely more powerful and aggressive after the battle. This was a strange, and subtle curiosity only caught by those who studied the Ancients' battles. For a very long time, it was simply referred to as the Dragon's Paradox.
It is consistent across every Ancient on record... Were they acting defeated to catch the other off-guard? Possibly, but how did their wounds heal? How did they become stronger?
The true discovery of Soul Fusion was nearly missed, mostly due to Soul Theory's very lagging development at the time. In the tail-end of the times, just before the Dark Era, the first Soul was manifested by direct magical manipulation. This was a major moment for the theory of a Soul's functions, and it was then that a connection was made by several drakologists to what could be occuring during the Ancients' battles.
As one Ancient absorbs the Soul of another, much of the power is utilized to heal their wounds, and any excess turns into raw magical power for the creature. This means that the stronger an opponent for a given Dragon, the more they will benefit from defeating that opponent. This is thought to explain how intruding Ancients could destroy a village with ease after battling with it's Guardian, no matter the damage incurred.
Soul Fusion Among Mortals
"So," I hear you saying, "I have a Soul. You have a Soul. I could kill you and become immensely powerful?" Not quite. You are right about becoming very powerful, even from an old Soul like me. But it does not work the same for mortals.
Even rarer than observations of natural Soul Fusion are those of Soul Fusion among mortals. It was believed to be possible, but most were unsure of the necessary circumstances, as it was also thought that the reason Ancients could even perform Soul Fusion in the first place was due to the situations they were in at the time, a life-or-death battle.
In the modern day, it is known to be very possible, though only between two individuals who have a strong connection, and no duel required. The practice has been outlawed, however, as it is not fully understood how one's Soul behaves upon fusing.