Roidmude's Core

The Roidmude's Core (ロイミュードのコア), also known simply as Cores (コア), are the essence of the Roidmudes that appear as their given numbers which distinguish themselves from each other (and are pronounced individually; i.e., 029 is Zero-Two-Nine), to which literally ties into their life, acting as their 'soul'. The destruction of a Roidmude's Core results in the permanent death of the Roidmude in question, but if their Core can survive the destruction of their body and be restored later.

Reviving Roidmudes via Cores
Should a Roidmude's Core survive and escape the destruction of it's body, it can fall into the hands of the Roidmude organization, which has several sources for preserving and subsequently reviving Roidmudes.
 * A Roidmude's Core can be absorbed into a Viral Core which matches their Low-Class animal motif. This was performed by Heart who provided a Cobra-Type Viral Core for Roidmude 029 who re-emerged soon after, allowing him to continue and successfully achieve his evolution into an Advanced Roidmude.
 * The tablet device possessed by Brain can, as well as preserving a Roidmude's Core, initiate a reset after absorbing the Core. This was performed on Roidmude 051, a rogue Roidmude whose actions risked compromising their operations and thus was executed by Chase.
 * Medic, who serves as a healer of the Roidmudes, can absorb a damaged Roidmude Core long enough for her to transport it out of harm's way so she can heal the Roidmude and help it reclaim its body uninterrupted. She first performed this on the Gunman Roidmude (017), restoring him shortly after his first destruction at the hands of Kamen Rider Mach, this process was not a reset and allowed 018 to retain his evolved form.

Destroying Cores
The only known way to permanently defeat a Roidmude via the destruction of their Cores is the power of Kamen Riders Drive and Mach, normally via their Full Throttle finishing attacks performed using the Shift Cars and Signal Bikes respectively, but also includes vehicles such as Drive's car, Tridoron. It is still possible for Cores to occasionally survive the destruction of their bodies, though this can be averted by following it up with a direct attack on their Cores before they escape.

The first Kamen Rider created by Krim Steinbelt, Proto-Drive, had the power to destroy Roidmude bodies but was unable to destroy their Cores. After being defeated by the Roidmudes, Proto-Drive was converted into Mashin Chaser who is tasked with destroying rogue Roidmudes while leaving their Cores intact, however, it is unknown if Mashin Chaser possesses the ability to destroy Cores, though he likely cannot.

Roidmudes by Core history

 * Roidmude 005: 005's Core survived his first destruction at the hands of Proto-Drive, due to his inability to destroy Roidmude Cores, allowing him to re-emerge in his Low-Class Bat-Type form. Months later, he was destroyed at the hands of Shift Cars controlled by the second Kamen Rider Drive.
 * Roidmude 006: 006's Core survived his first destruction at the hands of the Shift Cars during the Global Freeze.
 * Roidmude 010: Following his evolution into the Paint Roidmude, 010 was permanently destroyed by Kamen Rider Drive Type Speed Vegas' Dream Vegas Full Throttle with the Handle-Ken.
 * Roidmude 012: 012's Core survived his first destruction at the hands of the Shift Cars during the Global Freeze.
 * Roidmude 017: 017's Core survived his first destruction at the hands of Kamen Rider Mach thanks to Medic, who restored him to full health. He was later permanently defeated alongside his "little brother" Roidmude 018, having already had their bodies destroyed by Mach, who followed it up with an Magarl-influenced shot from the Zenrin Shooter which intercepted their Cores before they could escape.
 * Roidmude 018: 018's Core was destroyed alongside Roidmude 017, having already had their bodies destroyed by Mach, who followed it up with  an Magarl-influenced shot from the Zenrin Shooter  which intercepted their Cores before they could escape.
 * Roidmude 023: Following his evolution into the Crush Roidmude, 023 was permanently destroyed by Kamen Rider Drive Type Wild's Drift Slash with the Handle-Ken.
 * Roidmude 024: Following his evolution into the Volt Roidmude, 024's body and Core was destroyed by Kamen Rider Drive Type Technic Gravity's PerfecShot with the Door-Ju. However, Volt was able to bring himself back as a ghost thanks to a special device which he created.  Later, both the device and his copy were destroyed.
 * Roidmude 029: 029's Core managed to escape a battle with Drive which resulted in the destruction of two of his fellow Roidmudes, retreating to Heart who provided a Cobra-Type Viral Core for him. Re-emerging soon after, he continued and successfully achieved his evolution into the Iron Roidmude before being permanently destroyed by Drive Type Speed Hunter's JustiSmash.
 * Roidmude 037: 037's Core was destroyed along with his body in a fight with Drive with the Wild Full Throttle with the Handle-Ken.
 * Roidmude 051: Following his execution at the hands of Mashin Chaser, 051's Core was absorbed into Brain's tablet device and slated for a reset.
 * Roidmude 060: 060's Core was destroyed along with his body in a fight with Drive Type Speed's Speed Full Throttle with the Handle-Ken.
 * Roidmude 066: 066's Core survived his first destruction at the hands of the Shift Cars during the Global Freeze.
 * Roidmude 069: 069's Core was destroyed following his Giant Bat Roidmude body's destruction by Mach piloting the Ride Crosser, it plowing through the Core as it fell to the ground.
 * Roidmude 071: 071's Core was destroyed alongside 093, crushed under the wheels of Tridoron, shortly after they were defeated in a chase with the car.
 * Roidmude 074: Following his transformation into a Giant Cobra Roidmude, 074 was permanently destroyed by Kamen Rider Drive.
 * Roidmude 084: 084's Core was destroyed along with his body in a fight with Drive.
 * Roidmude 093: 093's Core was destroyed alongside 071, crushed under the wheels of Tridoron, shortly after they were defeated in a chase with the car.
 * Roidmude 096：096's Core was destroyed by Drive and Mach.
 * Roidmude 103: Mortally wounded by Drive in battle, 103 was able to give Heart the means to revive Medic before sucuumbing to his injuries, with both his body and Core being destroyed in an non-explosive manner.